How to be correct, lazy and efficient ?

Abstract: This paper is an introduction to Lambdix, a lazy Lisp interpreter implemented at the Research Laboratory of Paris XI University (Laboratoire de Recherche en Informatique, Orsay). Lambdix was devised in the course of an investigation into the relationship between the semantics of programming languages and their implementation; it was used to demonstrate that in the Lisp domain, semantic correctness is consistent with efficiency, contrary to what has often been claimed. The first part of the paper is an overview of well-known semantic difficulties encountered by Lisp as well as an informal presentation of Lambdix; it is shown that the difficulties which Lisp encouters do not arise in Lambdix. The second part is about efficiency in implementation models. It explains why Lambdix is better suited for lazy evaluation than previous models. The section ends by giving comparative execution time tables.


Closed form solutions for symmetric water filling games

Abstract: We study power control in optimization and game frameworks. In the optimization framework there is a single decision maker who assigns network resources and in the game framework users share the network resources according to Nash equilibrium. The solution of these problems is based on so-called water-filling technique, which in turn uses bisection method for solution of non-linear equations for Lagrange multiplies. Here we provide a closed form solution to the water-filling problem, which allows us to solve it in a finite number of operations. Also, we produce a closed form solution for the Nash equilibrium in symmetric Gaussian interference game with an arbitrary number of users. Even though the game is symmetric, there is an intrinsic hierarchical structure induced by the quantity of the resources available to the users. We use this hierarchical structure to perform a successive reduction of the game. In addition, to its mathematical beauty, the explicit solution allows one to study limiting cases when the crosstalk coefficient is either small or large. We provide an alternative simple proof of the convergence of the Iterative Water Filling Algorithm. Furthermore, it turns out that the convergence of Iterative Water Filling Algorithm slows down when the crosstalk coefficient is large. Using the closed form solution, we can avoid this problem. Finally, we compare the non-cooperative approach with the cooperative approach and show that the non-cooperative approach results in a more fair resource distribution.


Learning Probabilistic Models of Word Sense Disambiguation

Abstract: This dissertation presents several new methods of supervised and unsupervised learning of word sense disambiguation models. The supervised methods focus on performing model searches through a space of probabilistic models, and the unsupervised methods rely on the use of Gibbs Sampling and the Expectation Maximization (EM) algorithm. In both the supervised and unsupervised case, the Naive Bayesian model is found to perform well. An explanation for this success is presented in terms of learning rates and bias-variance decompositions.


Clifford Algebra of the Vector Space of Conics for decision boundary Hyperplanes in m-Euclidean Space

Abstract: In this paper we embed $m$-dimensional Euclidean space in the geometric algebra $Cl_m $ to extend the operators of incidence in ${R^m}$ to operators of incidence in the geometric algebra to generalize the notion of separator to a decision boundary hyperconic in the Clifford algebra of hyperconic sections denoted as ${Cl}({Co}_{2})$. This allows us to extend the concept of a linear perceptron or the spherical perceptron in conformal geometry and introduce the more general conic perceptron, namely the {elliptical perceptron}. Using Clifford duality a vector orthogonal to the decision boundary hyperplane is determined. Experimental results are shown in 2-dimensional Euclidean space where we separate data that are naturally separated by some typical plane conic separators by this procedure. This procedure is more general in the sense that it is independent of the dimension of the input data and hence we can speak of the hyperconic elliptic perceptron.


One-way Hash Function Based on Neural Network

Abstract: A hash function is constructed based on a three-layer neural network. The three neuron-layers are used to realize data confusion, diffusion and compression respectively, and the multi-block hash mode is presented to support the plaintext with variable length. Theoretical analysis and experimental results show that this hash function is one-way, with high key sensitivity and plaintext sensitivity, and secure against birthday attacks or meet-in-the-middle attacks. Additionally, the neural network's property makes it practical to realize in a parallel way. These properties make it a suitable choice for data signature or authentication.


Services within a busy period of an M/M/1 queue and Dyck paths

Abstract: We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with (n+1) customers.


Parsimony Principles for Software Components and Metalanguages

Abstract: Software is a communication system. The usual topic of communication is program behavior, as encoded by programs. Domain-specific libraries are codebooks, domain-specific languages are coding schemes, and so forth. To turn metaphor into method, we adapt toolsfrom information theory--the study of efficient communication--to probe the efficiency with which languages and libraries let us communicate programs. In previous work we developed an information-theoretic analysis of software reuse in problem domains. This new paper uses information theory to analyze tradeoffs in the design of components, generators, and metalanguages. We seek answers to two questions: (1) How can we judge whether a component is over- or under-generalized? Drawing on minimum description length principles, we propose that the best component yields the most succinct representation of the use cases. (2) If we view a programming language as an assemblage of metalanguages, each providing a complementary style of abstraction, how can these metalanguages aid or hinder us in efficiently describing software? We describe a complex triangle of interactions between the power of an abstraction mechanism, the amount of reuse it enables, and the cognitive difficulty of its use.


Reductionism, emergence, and levels of abstractions

Abstract: Can there be independent higher level laws of nature if everything is reducible to the fundamental laws of physics? The computer science notion of level of abstraction explains why there can -- illustrating how computational thinking can solve one of philosophy's most vexing problems.


Complexity of Propositional Proofs under a Promise

Abstract: We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an explicitly specified function $\Lam$ in the number of variables $n$. To this end, we develop propositional proof systems under different measures of promises (that is, different $\Lam$) as extensions of resolution. This is done by augmenting resolution with axioms that, roughly, can eliminate sets of truth assignments defined by Boolean circuits. We then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: 1. Resolution has polynomial-size refutations for all unsatisfiable 3CNF formulas when the promise is $\eps\cd2^n$, for any constant $0<\eps<1$. 2. There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is $2^{\delta n}$ (and the number of clauses is $o(n^{3/2})$), for any constant $0<\delta<1$.


Star Unfolding Convex Polyhedra via Quasigeodesic Loops

Abstract: We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple (non-overlapping), planar polygon: cut along one shortest path from each vertex of P to Q, and cut all but one segment of Q.


A Leaf Recognition Algorithm for Plant Classification Using Probabilistic Neural Network

Abstract: In this paper, we employ Probabilistic Neural Network (PNN) with image and data processing techniques to implement a general purpose automated leaf recognition algorithm. 12 leaf features are extracted and orthogonalized into 5 principal variables which consist the input vector of the PNN. The PNN is trained by 1800 leaves to classify 32 kinds of plants with an accuracy greater than 90%. Compared with other approaches, our algorithm is an accurate artificial intelligence approach which is fast in execution and easy in implementation.


Spatial Aggregation: Data Model and Implementation

Abstract: Data aggregation in Geographic Information Systems (GIS) is only marginally present in commercial systems nowadays, mostly through ad-hoc solutions. In this paper, we first present a formal model for representing spatial data. This model integrates geographic data and information contained in data warehouses external to the GIS. We define the notion of geometric aggregation, a general framework for aggregate queries in a GIS setting. We also identify the class of summable queries, which can be efficiently evaluated by precomputing the overlay of two or more of the thematic layers involved in the query. We also sketch a language, denoted GISOLAP-QL, for expressing queries that involve GIS and OLAP features. In addition, we introduce Piet, an implementation of our proposal, that makes use of overlay precomputation for answering spatial queries (aggregate or not). Our experimental evaluation showed that for a certain class of geometric queries with or without aggregation, overlay precomputation outperforms R-tree-based techniques. Finally, as a particular application of our proposal, we study topological queries.


Blocking a transition in a Free Choice net and what it tells about its throughput

Abstract: In a live and bounded Free Choice Petri net, pick a non-conflicting transition. Then there exists a unique reachable marking in which no transition is enabled except the selected one. For a routed live and bounded Free Choice net, this property is true for any transition of the net. Consider now a live and bounded stochastic routed Free Choice net, and assume that the routings and the firing times are independent and identically distributed. Using the above results, we prove the existence of asymptotic firing throughputs for all transitions in the net. Furthermore the vector of the throughputs at the different transitions is explicitly computable up to a multiplicative constant.


Separation Logic for Small-step Cminor

Abstract: Cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning and we have designed a Separation Logic for Cminor. In this paper, we give a small-step semantics (instead of the big-step of the proved-correct compiler) that is motivated by the need to support future concurrent extensions. We detail a machine-checked proof of soundness of our Separation Logic. This is the first large-scale machine-checked proof of a Separation Logic w.r.t. a small-step semantics. The work presented in this paper has been carried out in the Coq proof assistant. It is a first step towards an environment in which concurrent Cminor programs can be verified using Separation Logic and also compiled by a proved-correct compiler with formal end-to-end correctness guarantees.


On sparse representations of linear operators and the approximation of matrix products

Abstract: Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under consideration is sparse is used to decrease the number of necessary measurements while controlling the approximation error. In this paper, we instead focus on applications in numerical analysis, by way of sparse representations of linear operators with the objective of minimizing the number of operations needed to perform basic operations (here, multiplication) on these operators. We represent a linear operator by a sum of rank-one operators, and show how a sparse representation that guarantees a low approximation error for the product can be obtained from analyzing an induced quadratic form. This construction in turn yields new algorithms for computing approximate matrix products.


Small weakly universal Turing machines

Abstract: We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines.


Image Authentication Based on Neural Networks

Abstract: Neural network has been attracting more and more researchers since the past decades. The properties, such as parameter sensitivity, random similarity, learning ability, etc., make it suitable for information protection, such as data encryption, data authentication, intrusion detection, etc. In this paper, by investigating neural networks' properties, the low-cost authentication method based on neural networks is proposed and used to authenticate images or videos. The authentication method can detect whether the images or videos are modified maliciously. Firstly, this chapter introduces neural networks' properties, such as parameter sensitivity, random similarity, diffusion property, confusion property, one-way property, etc. Secondly, the chapter gives an introduction to neural network based protection methods. Thirdly, an image or video authentication scheme based on neural networks is presented, and its performances, including security, robustness and efficiency, are analyzed. Finally, conclusions are drawn, and some open issues in this field are presented.


Note on edge-colored graphs and digraphs without properly colored cycles

Abstract: We study the following two functions: d(n,c) and $\vec{d}(n,c)$; d(n,c) ($\vec{d}(n,c)$) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and minimum monochromatic degree (out-degree) at least k has a properly colored cycle. Abouelaoualim et al. (2007) stated a conjecture which implies that d(n,c)=1. Using a recursive construction of c-edge-colored graphs with minimum monochromatic degree p and without properly colored cycles, we show that $d(n,c)\ge {1 \over c}(\log_cn -\log_c\log_cn)$ and, thus, the conjecture does not hold. In particular, this inequality significantly improves a lower bound on $\vec{d}(n,2)$ obtained by Gutin, Sudakov and Yeo in 1998.


Comments on the Reliability of Lawson and Hanson's Linear Distance Programming Algorithm: Subroutine LDP

Abstract: This brief paper: (1) Discusses strategies to generate random test cases that can be used to extensively test any Linear Distance Program (LDP) software. (2) Gives three numerical examples of input cases generated by this strategy that cause problems in the Lawson and Hanson LDP module. (3) Proposes, as a standard matter of acceptable implementation procedures, that (unless it is done internally in the software itself, but, in general, this seems to be much rarer than one would expect) all users should test the returned output from any LDP module for self-consistency since it incurs only a small amount of added computational overhead and it is not hard to do.


A Note on Shortest Developments

Abstract: De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer's approach one arrives at a proof that some developments are finite which in addition yields an effective reduction strategy computing shortest developments as well as a simple formula computing their length. The duality fails for general beta-reduction. Our results simplify previous work by Khasidashvili.


Why the relational data model can be considered as a formal basis for group operations in object-oriented systems

Abstract: Relational data model defines a specification of a type "relation". However, its simplicity does not mean that the system implementing this model must operate with structures having the same simplicity. We consider two principles allowing create a system which combines object-oriented paradigm (OOP) and relational data model (RDM) in one framework. The first principle -- "complex data in encapsulated domains" -- is well known from The Third Manifesto by Date and Darwen. The second principle --"data complexity in names"-- is the basis for a system where data are described as complex objects and uniquely represented as a set of relations. Names of these relations and names of their attributes are combinations of names entered in specifications of the complex objects. Below, we consider the main properties of such a system.


Quasi-stationary distributions as centrality measures of reducible graphs

Abstract: Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by introduction of uniform random jumps with some probability. Up to the present, there is no clear criterion for the choice this parameter. We propose to use parameter-free centrality measure which is based on the notion of quasi-stationary distribution. Specifically we suggest four quasi-stationary based centrality measures, analyze them and conclude that they produce approximately the same ranking. The new centrality measures can be applied in spam detection to detect ``link farms'' and in image search to find photo albums.


Efficient Divide-and-Conquer Implementations Of Symmetric FSAs

Abstract: A deterministic finite-state automaton (FSA) is an abstract sequential machine that reads the symbols comprising an input word one at a time. An FSA is symmetric if its output is independent of the order in which the input symbols are read, i.e., if the output is invariant under permutations of the input. We show how to convert a symmetric FSA A into an automaton-like divide-and-conquer process whose intermediate results are no larger than the size of A's memory. In comparison, a similar result for general FSA's has been long known via functional composition, but entails an exponential increase in memory size. The new result has applications to parallel processing and symmetric FSA networks.


An Application of Chromatic Prototypes

Abstract: This paper has been withdrawn.


Complementary algorithms for graphs and percolation

Abstract: A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed that uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high precision value of pc = 0.59274603(9) was thus obtained, by Mersenne twister, for the two dimensional square site percolation threshold.


Public Cluster : parallel machine with multi-block approach

Abstract: We introduce a new approach to enable an open and public parallel machine which is accessible for multi users with multi jobs belong to different blocks running at the same time. The concept is required especially for parallel machines which are dedicated for public use as implemented at the LIPI Public Cluster. We have deployed the simplest technique by running multi daemons of parallel processing engine with different configuration files specified for each user assigned to access the system, and also developed an integrated system to fully control and monitor the whole system over web. A brief performance analysis is also given for Message Parsing Interface (MPI) engine. It is shown that the proposed approach is quite reliable and affect the whole performances only slightly.


Introducing OPTO : Portal for Optical Communities in Indonesia

Abstract: Since January 1, 2005 we have launched "OPTO" Portal, a website dedicated to optical communities in Indonesia. The address of this portal is http://www.opto.lipi.go.id and is self-supporting managed and not for commercial purposes. Our aims in launching this portal are to benefit Internet facility in increasing the communities' scientific activity; to provide an online reference in Indonesian language for optics-based science and technology subjects; as well as to pioneer the communities' online activities with real impacts and benefits for our society. We will describe in the paper the features of this portal that can be utilized by all individuals or members of optical communities to store and share information and to build networks or partnership as well. We realized that this portal is still not popular and most of our aims are still not reached. This conference should be a good place for all of us to collaborate to properly utilize this portal for the advantages to the optical communities in Indonesia and our society at large.


Open and Free Cluster for Public

Abstract: We introduce the LIPI Public Cluster, the first parallel machine facility fully open for public and for free in Indonesia and surrounding countries. In this paper, we focus on explaining our globally new concept on open cluster, and how to realize and manage it to meet the users needs. We show that after 2 years trial running and several upgradings, the Public Cluster performs well and is able to fulfil all requirements as expected.


Real-time control and monitoring system for LIPI's Public Cluster

Abstract: We have developed a monitoring and control system for LIPI's Public Cluster. The system consists of microcontrollers and full web-based user interfaces for daily operation. It is argued that, due to its special natures, the cluster requires fully dedicated and self developed control and monitoring system. We discuss the implementation of using parallel port and dedicated micro-controller for this purpose. We also show that integrating such systems enables an autonomous control system based on the real time monitoring, for instance an autonomous power supply control based on the actual temperature, etc.


Resource Allocation in Public Cluster with Extended Optimization Algorithm

Abstract: We introduce an optimization algorithm for resource allocation in the LIPI Public Cluster to optimize its usage according to incoming requests from users. The tool is an extended and modified genetic algorithm developed to match specific natures of public cluster. We present a detail analysis of optimization, and compare the results with the exact calculation. We show that it would be very useful and could realize an automatic decision making system for public clusters.


ADS-Directory Services for Mobile Ad-Hoc Networks Based on an Information Market Model

Abstract: Ubiquitous computing based on small mobile devices using wireless communication links is becoming very attractive. The computational power and storage capacities provided allow the execution of sophisticated applications. Due to the fact that sharing of information is a central problem for distributed applications, the development of self organizing middleware services providing high level interfaces for information managing is essential. ADS is a directory service for mobile ad-hoc networks dealing with local and nearby information as well as providing access to distant information. The approach discussed throughout this paper is based upon the concept of information markets.


ADS as Information Management Service in an M-Learning Environment

Abstract: Leveraging the potential power of even small handheld devices able to communicate wirelessly requires dedicated support. In particular, collaborative applications need sophisticated assistance in terms of querying and exchanging different kinds of data. Using a concrete example from the domain of mobile learning, the general need for information dissemination is motivated. Subsequently, and driven by infrastructural conditions, realization strategies of an appropriate middleware service are discussed.


Network synchronizability analysis: the theory of subgraphs and complementary graphs

Abstract: In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network's corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.


Reconstruction of Protein-Protein Interaction Pathways by Mining Subject-Verb-Objects Intermediates

Abstract: The exponential increase in publication rate of new articles is limiting access of researchers to relevant literature. This has prompted the use of text mining tools to extract key biological information. Previous studies have reported extensive modification of existing generic text processors to process biological text. However, this requirement for modification had not been examined. In this study, we have constructed Muscorian, using MontyLingua, a generic text processor. It uses a two-layered generalization-specialization paradigm previously proposed where text was generically processed to a suitable intermediate format before domain-specific data extraction techniques are applied at the specialization layer. Evaluation using a corpus and experts indicated 86-90% precision and approximately 30% recall in extracting protein-protein interactions, which was comparable to previous studies using either specialized biological text processing tools or modified existing tools. Our study had also demonstrated the flexibility of the two-layered generalization-specialization paradigm by using the same generalization layer for two specialized information extraction tasks.


Virtual Environments for Training: From Individual Learning to Collaboration with Humanoids

Abstract: The next generation of virtual environments for training is oriented towards collaborative aspects. Therefore, we have decided to enhance our platform for virtual training environments, adding collaboration opportunities and integrating humanoids. In this paper we put forward a model of humanoid that suits both virtual humans and representations of real users, according to collaborative training activities. We suggest adaptations to the scenario model of our platform making it possible to write collaborative procedures. We introduce a mechanism of action selection made up of a global repartition and an individual choice. These models are currently being integrated and validated in GVT, a virtual training tool for maintenance of military equipments, developed in collaboration with the French company NEXTER-Group.


Edit and verify

Abstract: Automated theorem provers are used in extended static checking, where they are the performance bottleneck. Extended static checkers are run typically after incremental changes to the code. We propose to exploit this usage pattern to improve performance. We present two approaches of how to do so and a full solution.


Characterising Web Site Link Structure

Abstract: The topological structures of the Internet and the Web have received considerable attention. However, there has been little research on the topological properties of individual web sites. In this paper, we consider whether web sites (as opposed to the entire Web) exhibit structural similarities. To do so, we exhaustively crawled 18 web sites as diverse as governmental departments, commercial companies and university departments in different countries. These web sites consisted of as little as a few thousand pages to millions of pages. Statistical analysis of these 18 sites revealed that the internal link structure of the web sites are significantly different when measured with first and second-order topological properties, i.e. properties based on the connectivity of an individual or a pairs of nodes. However, examination of a third-order topological property that consider the connectivity between three nodes that form a triangle, revealed a strong correspondence across web sites, suggestive of an invariant. Comparison with the Web, the AS Internet, and a citation network, showed that this third-order property is not shared across other types of networks. Nor is the property exhibited in generative network models such as that of Barabasi and Albert.


A Portal Analysis for the Design of a Collaborative Research Environment for Students and Supervisors (CRESS) within the CSCR Domain

Abstract: In a previous paper the CSCR domain was defined. Here this is taken to the next stage where we consider the design of a particular Collaborative Research Environment to support Students and Supervisors CRESS. Following the CSCR structure a preliminary design for CRESS has been established and a portal framework analysis is undertaken in order to determine the most appropriate set of tools for its implementation.


On the Self-stabilization of Mobile Robots in Graphs

Abstract: Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The contribution of this paper is threefold. First, we present a new model for studying mobile entities in networks subject to transient faults. Our model differs from the classical robot model because robots have constraints about the paths they are allowed to follow, and from the classical agent model because the number of agents remains fixed throughout the execution of the protocol. Second, in this model, we study the possibility of designing self-stabilizing algorithms when those algorithms are run by mobile robots (or agents) evolving on a graph. We concentrate on the core building blocks of robot and agents problems: naming and leader election. Not surprisingly, when no constraints are given on the network graph topology and local execution model, both problems are impossible to solve. Finally, using minimal hypothesis with respect to impossibility results, we provide deterministic and probabilistic solutions to both problems, and show equivalence of these problems by an algorithmic reduction mechanism.


Modeling Visual Information Processing in Brain: A Computer Vision Point of View and Approach

Abstract: We live in the Information Age, and information has become a critically important component of our life. The success of the Internet made huge amounts of it easily available and accessible to everyone. To keep the flow of this information manageable, means for its faultless circulation and effective handling have become urgently required. Considerable research efforts are dedicated today to address this necessity, but they are seriously hampered by the lack of a common agreement about "What is information?" In particular, what is "visual information" - human's primary input from the surrounding world. The problem is further aggravated by a long-lasting stance borrowed from the biological vision research that assumes human-like information processing as an enigmatic mix of perceptual and cognitive vision faculties. I am trying to find a remedy for this bizarre situation. Relying on a new definition of "information", which can be derived from Kolmogorov's compexity theory and Chaitin's notion of algorithmic information, I propose a unifying framework for visual information processing, which explicitly accounts for the perceptual and cognitive image processing peculiarities. I believe that this framework will be useful to overcome the difficulties that are impeding our attempts to develop the right model of human-like intelligent image processing.


Nodally 3-connected planar graphs and convex combination mappings

Abstract: A convex combination mapping of a planar graph is a plane mapping in which the external vertices are mapped to the corners of a convex polygon and every internal vertex is a proper weighted average of its neighbours. If a planar graph is nodally 3-connected or triangulated then every such mapping is an embedding (Tutte, Floater). We give a simple characterisation of nodally 3-connected planar graphs, and generalise the above result to any planar graph which admits any convex embedding.


Near Optimal Broadcast with Network Coding in Large Sensor Networks

Abstract: We study efficient broadcasting for wireless sensor networks, with network coding. We address this issue for homogeneous sensor networks in the plane. Our results are based on a simple principle (IREN/IRON), which sets the same rate on most of the nodes (wireless links) of the network. With this rate selection, we give a value of the maximum achievable broadcast rate of the source: our central result is a proof of the value of the min-cut for such networks, viewed as hypergraphs. Our metric for efficiency is the number of transmissions necessary to transmit one packet from the source to every destination: we show that IREN/IRON achieves near optimality for large networks; that is, asymptotically, nearly every transmission brings new information from the source to the receiver. As a consequence, network coding asymptotically outperforms any scheme that does not use network coding.


An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines

Abstract: This paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account: on the basis of prescribed kinetostatic performances, the workspace is analysed to find out the largest regular dextrous workspace enclosed in the Cartesian workspace. An algorithm describing this method is introduced. Two 3-DOF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second one features three linear joints which are mounted in parallel. In both cases, the mobile platform moves in the Cartesian x-y-z space with fixed orientation.


A Practical Ontology for the Large-Scale Modeling of Scholarly Artifacts and their Usage

Abstract: The large-scale analysis of scholarly artifact usage is constrained primarily by current practices in usage data archiving, privacy issues concerned with the dissemination of usage data, and the lack of a practical ontology for modeling the usage domain. As a remedy to the third constraint, this article presents a scholarly ontology that was engineered to represent those classes for which large-scale bibliographic and usage data exists, supports usage research, and whose instantiation is scalable to the order of 50 million articles along with their associated artifacts (e.g. authors and journals) and an accompanying 1 billion usage events. The real world instantiation of the presented abstract ontology is a semantic network model of the scholarly community which lends the scholarly process to statistical analysis and computational support. We present the ontology, discuss its instantiation, and provide some example inference rules for calculating various scholarly artifact metrics.


A Deterministic Sub-linear Time Sparse Fourier Algorithm via Non-adaptive Compressed Sensing Methods

Abstract: We study the problem of estimating the best B term Fourier representation for a given frequency-sparse signal (i.e., vector) $\textbf{A}$ of length $N \gg B$. More explicitly, we investigate how to deterministically identify B of the largest magnitude frequencies of $\hat{\textbf{A}}$, and estimate their coefficients, in polynomial$(B,\log N)$ time. Randomized sub-linear time algorithms which have a small (controllable) probability of failure for each processed signal exist for solving this problem. However, for failure intolerant applications such as those involving mission-critical hardware designed to process many signals over a long lifetime, deterministic algorithms with no probability of failure are highly desirable. In this paper we build on the deterministic Compressed Sensing results of Cormode and Muthukrishnan (CM) \cite{CMDetCS3,CMDetCS1,CMDetCS2} in order to develop the first known deterministic sub-linear time sparse Fourier Transform algorithm suitable for failure intolerant applications. Furthermore, in the process of developing our new Fourier algorithm, we present a simplified deterministic Compressed Sensing algorithm which improves on CM's algebraic compressibility results while simultaneously maintaining their results concerning exponential decay.


Cost-minimising strategies for data labelling : optimal stopping and active learning

Abstract: Supervised learning deals with the inference of a distribution over an output or label space $\CY$ conditioned on points in an observation space $\CX$, given a training dataset $D$ of pairs in $\CX \times \CY$. However, in a lot of applications of interest, acquisition of large amounts of observations is easy, while the process of generating labels is time-consuming or costly. One way to deal with this problem is {\em active} learning, where points to be labelled are selected with the aim of creating a model with better performance than that of an model trained on an equal number of randomly sampled points. In this paper, we instead propose to deal with the labelling cost directly: The learning goal is defined as the minimisation of a cost which is a function of the expected model performance and the total cost of the labels used. This allows the development of general strategies and specific algorithms for (a) optimal stopping, where the expected cost dictates whether label acquisition should continue (b) empirical evaluation, where the cost is used as a performance metric for a given combination of inference, stopping and sampling methods. Though the main focus of the paper is optimal stopping, we also aim to provide the background for further developments and discussion in the related field of active learning.


Achievable Outage Rates with Improved Decoding of Bicm Multiband Ofdm Under Channel Estimation Errors

Abstract: We consider the decoding of bit interleaved coded modulation (BICM) applied to multiband OFDM for practical scenarios where only a noisy (possibly very bad) estimate of the channel is available at the receiver. First, a decoding metric based on the channel it a posteriori probability density, conditioned on the channel estimate is derived and used for decoding BICM multiband OFDM. Then, we characterize the limits of reliable information rates in terms of the maximal achievable outage rates associated to the proposed metric. We also compare our results with the outage rates of a system using a theoretical decoder. Our results are useful for designing a communication system where a prescribed quality of service (QoS), in terms of achievable target rates with small error probability, must be satisfied even in the presence of imperfect channel estimation. Numerical results over both realistic UWB and theoretical Rayleigh fading channels show that the proposed method provides significant gain in terms of BER and outage rates compared to the classical mismatched detector, without introducing any additional complexity.


On Optimal Turbo Decoding of Wideband MIMO-OFDM Systems Under Imperfect Channel State Information

Abstract: We consider the decoding of bit interleaved coded modulation (BICM) applied to both multiband and MIMO OFDM systems for typical scenarios where only a noisy (possibly very bad) estimate of the channel is provided by sending a limited number of pilot symbols. First, by using a Bayesian framework involving the channel a posteriori density, we adopt a practical decoding metric that is robust to the presence of channel estimation errors. Then this metric is used in the demapping part of BICM multiband and MIMO OFDM receivers. We also compare our results with the performance of a mismatched decoder that replaces the channel by its estimate in the decoding metric. Numerical results over both realistic UWB and theoretical Rayleigh fading channels show that the proposed method provides significant gain in terms of bit error rate compared to the classical mismatched detector, without introducing any additional complexity.


Wavelet Based Semi-blind Channel Estimation For Multiband OFDM

Abstract: This paper introduces an expectation-maximization (EM) algorithm within a wavelet domain Bayesian framework for semi-blind channel estimation of multiband OFDM based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response in order to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding ``unsignificant'' wavelet coefficients from the estimation process. Simulation results using UWB channels issued from both models and measurements show that under sparsity conditions, the proposed algorithm outperforms pilot based channel estimation in terms of mean square error and bit error rate and enhances the estimation accuracy with less computational complexity than traditional semi-blind methods.


MIMO-OFDM Optimal Decoding and Achievable Information Rates Under Imperfect Channel Estimation

Abstract: Optimal decoding of bit interleaved coded modulation (BICM) MIMO-OFDM where an imperfect channel estimate is available at the receiver is investigated. First, by using a Bayesian approach involving the channel a posteriori density, we derive a practical decoding metric for general memoryless channels that is robust to the presence of channel estimation errors. Then, we evaluate the outage rates achieved by a decoder that uses our proposed metric. The performance of the proposed decoder is compared to the classical mismatched decoder and a theoretical decoder defined as the best decoder in the presence of imperfect channel estimation. Numerical results over Rayleigh block fading MIMO-OFDM channels show that the proposed decoder outperforms mismatched decoding in terms of bit error rate and outage capacity without introducing any additional complexity.


Valid formulas, games and network protocols

Abstract: We describe a remarkable relation between the notion of valid formula of predicate logic and the specification of network protocols. We give several examples such as the acknowledgement of one packet or of a sequence of packets. We show how to specify the composition of protocols.


A Light-Based Device for Solving the Hamiltonian Path Problem

Abstract: In this paper we suggest the use of light for performing useful computations. Namely, we propose a special device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.


Defensive forecasting for optimal prediction with expert advice

Abstract: The method of defensive forecasting is applied to the problem of prediction with expert advice for binary outcomes. It turns out that defensive forecasting is not only competitive with the Aggregating Algorithm but also handles the case of "second-guessing" experts, whose advice depends on the learner's prediction; this paper assumes that the dependence on the learner's prediction is continuous.


Solving the Hamiltonian path problem with a light-based computer

Abstract: In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.


A Data-Parallel Version of Aleph

Abstract: This is to present work on modifying the Aleph ILP system so that it evaluates the hypothesised clauses in parallel by distributing the data-set among the nodes of a parallel or distributed machine. The paper briefly discusses MPI, the interface used to access message- passing libraries for parallel computers and clusters. It then proceeds to describe an extension of YAP Prolog with an MPI interface and an implementation of data-parallel clause evaluation for Aleph through this interface. The paper concludes by testing the data-parallel Aleph on artificially constructed data-sets.


Resolution over Linear Equations and Multilinear Proofs

Abstract: We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using the (monotone) interpolation by a communication game technique we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (non-monotone) interpolants in this fragment. We then apply these results to extend and improve previous results on multilinear proofs (over fields of characteristic 0), as studied in [RazTzameret06]. Specifically, we show the following: 1. Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations. 2. Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the \emph{functional} pigeonhole principle. The latter are different than previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system.


Learning Phonotactics Using ILP

Abstract: This paper describes experiments on learning Dutch phonotactic rules using Inductive Logic Programming, a machine learning discipline based on inductive logical operators. Two different ways of approaching the problem are experimented with, and compared against each other as well as with related work on the task. The results show a direct correspondence between the quality and informedness of the background knowledge and the constructed theory, demonstrating the ability of ILP to take good advantage of the prior domain knowledge available. Further research is outlined.


Homogeneous temporal activity patterns in a large online communication space

Abstract: The many-to-many social communication activity on the popular technology-news website Slashdot has been studied. We have concentrated on the dynamics of message production without considering semantic relations and have found regular temporal patterns in the reaction time of the community to a news-post as well as in single user behavior. The statistics of these activities follow log-normal distributions. Daily and weekly oscillatory cycles, which cause slight variations of this simple behavior, are identified. A superposition of two log-normal distributions can account for these variations. The findings are remarkable since the distribution of the number of comments per users, which is also analyzed, indicates a great amount of heterogeneity in the community. The reader may find surprising that only a few parameters allow a detailed description, or even prediction, of social many-to-many information exchange in this kind of popular public spaces.


Designing a Collaborative Research Environment for Students and their Supervisors (CRESS)

Abstract: In a previous paper the CSCR domain was defined. Here this is taken to the next stage where the design of a particular Collaborative Research Environment to support Students and Supervisors (CRESS) is considered. Following the CSCR structure this paper deals with an analysis of 13 collaborative working environments to determine a preliminary design for CRESS in order to discover the most appropriate set of tools for its implementation.


Hybrid Branching-Time Logics

Abstract: Hybrid branching-time logics are introduced as extensions of CTL-like logics with state variables and the downarrow-binder. Following recent work in the linear framework, only logics with a single variable are considered. The expressive power and the complexity of satisfiability of the resulting logics is investigated. As main result, the satisfiability problem for the hybrid versions of several branching-time logics is proved to be 2EXPTIME-complete. These branching-time logics range from strict fragments of CTL to extensions of CTL that can talk about the past and express fairness-properties. The complexity gap relative to CTL is explained by a corresponding succinctness result. To prove the upper bound, the automata-theoretic approach to branching-time logics is extended to hybrid logics, showing that non-emptiness of alternating one-pebble Buchi tree automata is 2EXPTIME-complete.


Design: One, but in different forms

Abstract: This overview paper defends an augmented cognitively oriented generic-design hypothesis: there are both significant similarities between the design activities implemented in different situations and crucial differences between these and other cognitive activities; yet, characteristics of a design situation (related to the design process, the designers, and the artefact) introduce specificities in the corresponding cognitive activities and structures that are used, and in the resulting designs. We thus augment the classical generic-design hypothesis with that of different forms of designing. We review the data available in the cognitive design research literature and propose a series of candidates underlying such forms of design, outlining a number of directions requiring further elaboration.


On Edge-Disjoint Pairs Of Matchings

Abstract: For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We show that 5/4 is a tight upper bound for |M|/|H|.


Lower Bounds for the Complexity of the Voronoi Diagram of Polygonal Curves under the Discrete Frechet Distance

Abstract: We give lower bounds for the combinatorial complexity of the Voronoi diagram of polygonal curves under the discrete Frechet distance. We show that the Voronoi diagram of n curves in R^d with k vertices each, has complexity Omega(n^{dk}) for dimension d=1,2 and Omega(n^{d(k-1)+2}) for d>2.


Exact Cover with light

Abstract: We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.


Solving the subset-sum problem with a light-based device

Abstract: We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants).


Who is the best connected EC researcher? Centrality analysis of the complex network of authors in evolutionary computation

Abstract: Co-authorship graphs (that is, the graph of authors linked by co-authorship of papers) are complex networks, which expresses the dynamics of a complex system. Only recently its study has started to draw interest from the EC community, the first paper dealing with it having been published two years ago. In this paper we will study the co-authorship network of EC at a microscopic level. Our objective is ascertaining which are the most relevant nodes (i.e. authors) in it. For this purpose, we examine several metrics defined in the complex-network literature, and analyze them both in isolation and combined within a Pareto-dominance approach. The result of our analysis indicates that there are some well-known researchers that appear systematically in top rankings. This also provides some hints on the social behavior of our community.


Repairing Inconsistent XML Write-Access Control Policies

Abstract: XML access control policies involving updates may contain security flaws, here called inconsistencies, in which a forbidden operation may be simulated by performing a sequence of allowed operations. This paper investigates the problem of deciding whether a policy is consistent, and if not, how its inconsistencies can be repaired. We consider policies expressed in terms of annotated DTDs defining which operations are allowed or denied for the XML trees that are instances of the DTD. We show that consistency is decidable in PTIME for such policies and that consistent partial policies can be extended to unique "least-privilege" consistent total policies. We also consider repair problems based on deleting privileges to restore consistency, show that finding minimal repairs is NP-complete, and give heuristics for finding repairs.


Attribute Estimation and Testing Quasi-Symmetry

Abstract: A Boolean function is symmetric if it is invariant under all permutations of its arguments; it is quasi-symmetric if it is symmetric with respect to the arguments on which it actually depends. We present a test that accepts every quasi-symmetric function and, except with an error probability at most delta>0, rejects every function that differs from every quasi-symmetric function on at least a fraction epsilon>0 of the inputs. For a function of n arguments, the test probes the function at O((n/epsilon)\log(n/delta)) inputs. Our quasi-symmetry test acquires information concerning the arguments on which the function actually depends. To do this, it employs a generalization of the property testing paradigm that we call attribute estimation. Like property testing, attribute estimation uses random sampling to obtain results that have only "one-sided'' errors and that are close to accurate with high probability.


Provenance as Dependency Analysis

Abstract: Provenance is information recording the source, derivation, or history of some information. Provenance tracking has been studied in a variety of settings; however, although many design points have been explored, the mathematical or semantic foundations of data provenance have received comparatively little attention. In this paper, we argue that dependency analysis techniques familiar from program analysis and program slicing provide a formal foundation for forms of provenance that are intended to show how (part of) the output of a query depends on (parts of) its input. We introduce a semantic characterization of such dependency provenance, show that this form of provenance is not computable, and provide dynamic and static approximation techniques.


Collection analysis for Horn clause programs

Abstract: We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to provide partial correctness properties of logic programs. For example, one might wish to specify than whenever the atom $sort(t,s)$ is proved then the two lists $t$ and $s$ contain the same multiset of items (that is, $s$ is a permutation of $t$). If sorting removes duplicates, then one would like to infer that the sets of items underlying $t$ and $s$ are the same. Such results could be useful to have if they can be determined statically and automatically. We present a scheme by which such collection analysis can be structured and automated. Central to this scheme is the use of linear logic as a omputational logic underlying the logic of Horn clauses.


Focusing and Polarization in Intuitionistic Logic

Abstract: A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof search and the proof normalization approaches to computation. Various proof systems in literature exhibit characteristics of focusing to one degree or another. We present a new, focused proof system for intuitionistic logic, called LJF, and show how other proof systems can be mapped into the new system by inserting logical connectives that prematurely stop focusing. We also use LJF to design a focused proof system for classical logic. Our approach to the design and analysis of these systems is based on the completeness of focusing in linear logic and on the notion of polarity that appears in Girard's LC and LU proof systems.


A Language for Generic Programming in the Large

Abstract: Generic programming is an effective methodology for developing reusable software libraries. Many programming languages provide generics and have features for describing interfaces, but none completely support the idioms used in generic programming. To address this need we developed the language G. The central feature of G is the concept, a mechanism for organizing constraints on generics that is inspired by the needs of modern C++ libraries. G provides modular type checking and separate compilation (even of generics). These characteristics support modular software development, especially the smooth integration of independently developed components. In this article we present the rationale for the design of G and demonstrate the expressiveness of G with two case studies: porting the Standard Template Library and the Boost Graph Library from C++ to G. The design of G shares much in common with the concept extension proposed for the next C++ Standard (the authors participated in its design) but there are important differences described in this article.


The study of a new gerrymandering methodology

Abstract: This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different standards of the "simple" shape. The first standard is that the final shape of the congressional districts should be of a simplest figure and we apply a modified "shortest split line algorithm" where the factor of the same population is considered only. The second standard is that the gerrymandering should ensure the integrity of the current administrative area as the convenience for management. Thus we combine the factor of the administrative area with the first standard, and generate an improved model resulting in the new diagram in which the perimeters of the districts are along the boundaries of some current counties. Moreover, the gerrymandering should consider the geographic features.The third standard is introduced to describe this situation. Finally, it can be proved that the difference between the supporting ratio of a certain party in each district and the average supporting ratio of that particular party in the whole state obeys the Chi-square distribution approximately. Consequently, we can obtain an archetypal formula to check whether the gerrymandering we propose is fair.


Compositional Semantics Grounded in Commonsense Metaphysics

Abstract: We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. Assuming the existence of such a structure, we show that the semantics of various natural language phenomena may become nearly trivial.


On Compact Routing for the Internet

Abstract: While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''


Unsatisfiable Linear k-CNFs Exist, for every k

Abstract: We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every clause has size exactly k. It was known that for k >= 3, Linear k-SAT is NP-complete if and only if an unsatisfiable linear k-CNF formula exists, and that they do exist for k >= 4. We prove that unsatisfiable linear k-CNF formulas exist for every k. Let f(k) be the minimum number of clauses in an unsatisfiable linear k-CNF formula. We show that f(k) is Omega(k2^k) and O(4^k*k^4), i.e., minimum size unsatisfiable linear k-CNF formulas are significantly larger than minimum size unsatisfiable k-CNF formulas. Finally, we prove that, surprisingly, linear k-CNF formulas do not allow for a larger fraction of clauses to be satisfied than general k-CNF formulas.


Randomized algorithm for the k-server problem on decomposable spaces

Abstract: We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log k). This method yields o(k)-competitive algorithms solving the randomized k-server problem, for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree). HSTs are important tools for probabilistic approximation of metric spaces.


Continuous and randomized defensive forecasting: unified view

Abstract: Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous manner and which produces deterministic forecasts, and "randomized", in which the dependence of Sceptic's moves on the forecasts is arbitrary and Forecaster's moves are allowed to be randomized. This note shows that the randomized variety can be obtained from the continuous variety by smearing Sceptic's moves to make them continuous.


On a constructive characterization of a class of trees related to pairs of disjoint matchings

Abstract: For a graph consider the pairs of disjoint matchings which union contains as many edges as possible, and define a parameter $\alpha$ which eqauls the cardinality of the largest matching in those pairs. Also, define $\betta$ to be the cardinality of a maximum matching of the graph. We give a constructive characterization of trees which satisfy the $\alpha$=$\betta$ equality. The proof of our main theorem is based on a new decomposition algorithm obtained for trees.


Key Agreement and Authentication Schemes Using Non-Commutative Semigroups

Abstract: We give a new two-pass authentication scheme, whichis a generalisation of an authentication scheme of Sibert-Dehornoy-Girault based on the Diffie-Hellman conjugacy problem. Compared to the above scheme, for some parameters it is more efficient with respect to multiplications. We sketch a proof that our authentication scheme is secure. We give a new key agreement protocols.


On the AAGL Protocol

Abstract: Recently the AAGL (Anshel-Anshel-Goldfeld-Lemieux) has been proposed which can be used for RFID tags. We give algorithms for the problem (we call the MSCSPv) on which the security of the AAGL protocol is based upon. Hence we give various attacks for general parameters on the recent AAGL protocol proposed. One of our attacks is a deterministic algorithm which has space complexity and time complexity both atleast exponentialin the worst case. In a better case using a probabilistic algorithm the time complexity canbe O(|XSS(ui')^L5*(n^(1+e)) and the space complexity can be O(|XSS(ui')|^L6), where the element ui' is part of a public key, n is the index of braid group, XSS is a summit type set and e is a constant in a limit. The above shows the AAGL protocol is potentially not significantly more secure as using key agreement protocols based on the conjugacy problem such as the AAG (Anshel-Anshel-Goldfeld) protocol because both protocols can be broken with complexity which do not significantly differ. We think our attacks can be improved.


User Participation in Social Media: Digg Study

Abstract: The social news aggregator Digg allows users to submit and moderate stories by voting on (digging) them. As is true of most social sites, user participation on Digg is non-uniformly distributed, with few users contributing a disproportionate fraction of content. We studied user participation on Digg, to see whether it is motivated by competition, fueled by user ranking, or social factors, such as community acceptance. For our study we collected activity data of the top users weekly over the course of a year. We computed the number of stories users submitted, dugg or commented on weekly. We report a spike in user activity in September 2006, followed by a gradual decline, which seems unaffected by the elimination of user ranking. The spike can be explained by a controversy that broke out at the beginning of September 2006. We believe that the lasting acrimony that this incident has created led to a decline of top user participation on Digg.


A structure from motion inequality

Abstract: We state an elementary inequality for the structure from motion problem for m cameras and n points. This structure from motion inequality relates space dimension, camera parameter dimension, the number of cameras and number points and global symmetry properties and provides a rigorous criterion for which reconstruction is not possible with probability 1. Mathematically the inequality is based on Frobenius theorem which is a geometric incarnation of the fundamental theorem of linear algebra. The paper also provides a general mathematical formalism for the structure from motion problem. It includes the situation the points can move while the camera takes the pictures.


On Ullman's theorem in computer vision

Abstract: Both in the plane and in space, we invert the nonlinear Ullman transformation for 3 points and 3 orthographic cameras. While Ullman's theorem assures a unique reconstruction modulo a reflection for 3 cameras and 4 points, we find a locally unique reconstruction for 3 cameras and 3 points. Explicit reconstruction formulas allow to decide whether picture data of three cameras seeing three points can be realized as a point-camera configuration.


Space and camera path reconstruction for omni-directional vision

Abstract: In this paper, we address the inverse problem of reconstructing a scene as well as the camera motion from the image sequence taken by an omni-directional camera. Our structure from motion results give sharp conditions under which the reconstruction is unique. For example, if there are three points in general position and three omni-directional cameras in general position, a unique reconstruction is possible up to a similarity. We then look at the reconstruction problem with m cameras and n points, where n and m can be large and the over-determined system is solved by least square methods. The reconstruction is robust and generalizes to the case of a dynamic environment where landmarks can move during the movie capture. Possible applications of the result are computer assisted scene reconstruction, 3D scanning, autonomous robot navigation, medical tomography and city reconstructions.


Minimum Cost Homomorphisms to Reflexive Digraphs

Abstract: For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$ such that $uv\in A(G)$ implies $f(u)f(v)\in A(H)$. If moreover each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of a homomorphism $f$ is $\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed digraph $H$, the {\em minimum cost homomorphism problem} for $H$, denoted MinHOM($H$), is the following problem. Given an input digraph $G$, together with costs $c_i(u)$, $u\in V(G)$, $i\in V(H)$, and an integer $k$, decide if $G$ admits a homomorphism to $H$ of cost not exceeding $k$. We focus on the minimum cost homomorphism problem for {\em reflexive} digraphs $H$ (every vertex of $H$ has a loop). It is known that the problem MinHOM($H$) is polynomial time solvable if the digraph $H$ has a {\em Min-Max ordering}, i.e., if its vertices can be linearly ordered by $<$ so that $i<j, s<r$ and $ir, js \in A(H)$ imply that $is \in A(H)$ and $jr \in A(H)$. We give a forbidden induced subgraph characterization of reflexive digraphs with a Min-Max ordering; our characterization implies a polynomial time test for the existence of a Min-Max ordering. Using this characterization, we show that for a reflexive digraph $H$ which does not admit a Min-Max ordering, the minimum cost homomorphism problem is NP-complete. Thus we obtain a full dichotomy classification of the complexity of minimum cost homomorphism problems for reflexive digraphs.


On the Complexity of the Minimum Cost Homomorphism Problem for Reflexive Multipartite Tournaments

Abstract: For digraphs $D$ and $H$, a mapping $f: V(D)\dom V(H)$ is a homomorphism of $D$ to $H$ if $uv\in A(D)$ implies $f(u)f(v)\in A(H).$ For a fixed digraph $H$, the homomorphism problem is to decide whether an input digraph $D$ admits a homomorphism to $H$ or not, and is denoted as HOMP($H$). Digraphs are allowed to have loops, but not allowed to have parallel arcs. A natural optimization version of the homomorphism problem is defined as follows. If each vertex $u \in V(D)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of the homomorphism $f$ is $\sum_{u\in V(D)}c_{f(u)}(u)$. For each fixed digraph $H$, we have the {\em minimum cost homomorphism problem for} $H$ and denote it as MinHOMP($H$). The problem is to decide, for an input graph $D$ with costs $c_i(u),$ $u \in V(D), i\in V(H)$, whether there exists a homomorphism of $D$ to $H$ and, if one exists, to find one of minimum cost. In a recent paper, we posed a problem of characterizing polynomial time solvable and NP-hard cases of the minimum cost homomorphism problem for acyclic multipartite tournaments with possible loops (w.p.l.). In this paper, we solve the problem for reflexive multipartite tournaments and demonstrate a considerate difficulty of the problem for the whole class of multipartite tournaments w.p.l. using, as an example, acyclic 3-partite tournaments of order 4 w.p.l.\footnote{This paper was submitted to Discrete Mathematics on April 6, 2007}


Complexity of the Minimum Cost Homomorphism Problem for Semicomplete Digraphs with Possible Loops

Abstract: For digraphs $D$ and $H$, a mapping $f: V(D)\dom V(H)$ is a homomorphism of $D$ to $H$ if $uv\in A(D)$ implies $f(u)f(v)\in A(H).$ For a fixed digraph $H$, the homomorphism problem is to decide whether an input digraph $D$ admits a homomorphism to $H$ or not, and is denoted as HOM($H$). An optimization version of the homomorphism problem was motivated by a real-world problem in defence logistics and was introduced in \cite{gutinDAM154a}. If each vertex $u \in V(D)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of the homomorphism $f$ is $\sum_{u\in V(D)}c_{f(u)}(u)$. For each fixed digraph $H$, we have the {\em minimum cost homomorphism problem for} $H$ and denote it as MinHOM($H$). The problem is to decide, for an input graph $D$ with costs $c_i(u),$ $u \in V(D), i\in V(H)$, whether there exists a homomorphism of $D$ to $H$ and, if one exists, to find one of minimum cost. Although a complete dichotomy classification of the complexity of MinHOM($H$) for a digraph $H$ remains an unsolved problem, complete dichotomy classifications for MinHOM($H$) were proved when $H$ is a semicomplete digraph \cite{gutinDAM154b}, and a semicomplete multipartite digraph \cite{gutinDAM}. In these studies, it is assumed that the digraph $H$ is loopless. In this paper, we present a full dichotomy classification for semicomplete digraphs with possible loops, which solves a problem in \cite{gutinRMS}.\footnote{This paper was submitted to SIAM J. Discrete Math. on October 27, 2006}


On the Security of the Cha-Ko-Lee-Han-Cheon Braid Group Public Key Cryptosystem

Abstract: We show that a number of cryptographic protocols using non-commutative semigroups including the Cha-Ko-Lee-Han-Cheon braid group public-key cryptosystem and related public-key cryptosystems such as the Shpilrain-Ushakov public-key cryptosystems are based on the MSCSP.


An Experimental Investigation of Secure Communication With Chaos Masking

Abstract: The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos generators. In the present work the phenomenon of secure communication with chaos masking has been investigated experimentally. In this investigation chaos which is generated from two chaos generators is masked with the massage signal to be transmitted, thus makes communication is more secure.


The universal evolutionary computer based on super-recursive algorithms of evolvability

Abstract: This work exposes which mechanisms and procesess in the Nature of evolution compute a function not computable by Turing machine. The computer with intelligence that is not higher than one bacteria population could have, but with efficency to solve the problems that are non-computable by Turing machine is represented. This theoretical construction is called Universal Evolutinary Computer and it is based on the superecursive algorithms of evolvability.


Aggregation Languages for Moving Object and Places of Interest Data

Abstract: We address aggregate queries over GIS data and moving object data, where non-spatial data are stored in a data warehouse. We propose a formal data model and query language to express complex aggregate queries. Next, we study the compression of trajectory data, produced by moving objects, using the notions of stops and moves. We show that stops and moves are expressible in our query language and we consider a fragment of this language, consisting of regular expressions to talk about temporally ordered sequences of stops and moves. This fragment can be used to efficiently express data mining and pattern matching tasks over trajectory data.


Integrating users' needs into multimedia information retrieval system

Abstract: The exponential growth of multimedia information and the development of various communication media generated new problems at various levels including the rate of flow of information, problems of storage and management. The difficulty which arises is no longer the existence of information but rather the access to this information. When designing multimedia information retrieval system, it is appropriate to bear in mind the potential users and their information needs. We assumed that multimedia information representation which takes into account explicitly the users' needs and the cases of use could contribute to the adaptation potentials of the system for the end-users. We believe also that responses of multimedia information system would be more relevant to the users' needs if the types of results to be used from the system were identified before the design and development of the system. We propose the integration of the users' information needs. More precisely integrating usage contexts of resulting information in an information system (during creation and feedback) should enhance more pertinent users' need. The first section of this study is dedicated to traditional multimedia information systems and specifically the approaches of representing multimedia information. Taking into account the dynamism of users, these approaches do not permit the explicit integration of the users' information needs. In this paper, we will present our proposals based on economic intelligence approach. This approach emphasizes the importance of starting any process of information retrieval witch the user information need.


Priority Queue Based on Multilevel Prefix Tree

Abstract: Tree structures are very often used data structures. Among ordered types of trees there are many variants whose basic operations such as insert, delete, search, delete-min are characterized by logarithmic time complexity. In the article I am going to present the structure whose time complexity for each of the above operations is $O(\frac{M}{K} + K)$, where M is the size of data type and K is constant properly matching the size of data type. Properly matched K will make the structure function as a very effective Priority Queue. The structure size linearly depends on the number and size of elements. PTrie is a clever combination of the idea of prefix tree -- Trie, structure of logarithmic time complexity for insert and remove operations, doubly linked list and queues.


The Fuzzy Vault for fingerprints is Vulnerable to Brute Force Attack

Abstract: The \textit{fuzzy vault} approach is one of the best studied and well accepted ideas for binding cryptographic security into biometric authentication. The vault has been implemented in connection with fingerprint data by Uludag and Jain. We show that this instance of the vault is vulnerable to brute force attack. An interceptor of the vault data can recover both secret and template data using only generally affordable computational resources. Some possible alternatives are then discussed and it is suggested that cryptographic security may be preferable to the one - way function approach to biometric security.


Explicit formulas for efficient multiplication in F_{3^{6m}}

Abstract: Efficient computation of the Tate pairing is an important part of pairing-based cryptography. Recently with the introduction of the Duursma-Lee method special attention has been given to the fields of characteristic 3. Especially multiplication in F_{3^{6m}}, where m is prime, is an important operation in the above method. In this paper we propose a new method to reduce the number of F_{3^m} multiplications for multiplication in F_{3^{6m}} from 18 in recent implementations to 15. The method is based on the fast Fourier tranmsform and explicit formulas are given. The execution times of our software implementations for F_{3^{6m}} show the efficiency of our results.


Efficient FPGA-based multipliers for F_{3^97} and F_{3^{6*97}}

Abstract: In this work we present a new structure for multiplication in finite fields. This structure is based on a digit-level LFSR (Linear Feedback Shift Register) multiplier in which the area of digit-multipliers are reduced using the Karatsuba method. We compare our results with the other works in the literature for F_{3^97}. We also propose new formulas for multiplication in F_{3^{6*97}}. These new formulas reduce the number of F_{3^97}-multiplications from 18 to 15. The fields F_{3^{97}} and F_{3^{6*97}} are relevant in the context of pairing-based cryptography.


Identifying Small Mean Reverting Portfolios

Abstract: Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability tradeoff and the impact of predictability in various markets.


Web Server Benchmark Application WiiBench using Erlang/OTP R11 and Fedora-Core Linux 5.0

Abstract: As the web grows and the amount of traffics on the web server increase, problems related to performance begin to appear. Some of the problems, such as the number of users that can access the server simultaneously, the number of requests that can be handled by the server per second (requests per second) to bandwidth consumption and hardware utilization like memories and CPU. To give better quality of service (\textbf{\textit{QoS}}), web hosting providers and also the system administrators and network administrators who manage the server need a benchmark application to measure the capabilities of their servers. Later, the application intends to work under Linux/Unix -- like platforms and built using Erlang/OTP R11 as a concurrent oriented language under Fedora Core Linux 5.0. \textbf{\textit{WiiBench}} is divided into two main parts, the controller section and the launcher section. Controller is the core of the application. It has several duties, such as read the benchmark scenario file, configure the program based on the scenario, initialize the launcher section, gather the benchmark results from local and remote Erlang node where the launcher runs and write them in a log file (later the log file will be used to generate a report page for the sysadmin). Controller also has function as a timer which act as timing for user inters arrival to the server. Launcher generates a number of users based on the scenario, initialize them and start the benchmark by sending requests to the web server. The clients also gather the benchmark result and send them to the controller.


A Dichotomy Theorem for General Minimum Cost Homomorphism Problem

Abstract: In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights $c_{va}$ for every variable $v$ and value $a$, and the aim is to find an assignment $f$ to the variables that minimizes $\sum_{v} c_{vf(v)}$. Let $MinHom(\Gamma)$ denote the $MinHom$ problem parameterized by the set of predicates allowed for constraints. $MinHom(\Gamma)$ is related to many well-studied combinatorial optimization problems, and concrete applications can be found in, for instance, defence logistics and machine learning. We show that $MinHom(\Gamma)$ can be studied by using algebraic methods similar to those used for CSPs. With the aid of algebraic techniques, we classify the computational complexity of $MinHom(\Gamma)$ for all choices of $\Gamma$. Our result settles a general dichotomy conjecture previously resolved only for certain classes of directed graphs, [Gutin, Hell, Rafiey, Yeo, European J. of Combinatorics, 2008].


Can Alice and Bob be random: a study on human playing zero knowledge protocols

Abstract: The research described in this abstract was initiated by discussions between the author and Giovanni Di Crescenzo in Barcelona in early 2004. It was during Advanced Course on Contemporary Cryptology that Di Crescenzo gave a course on zero knowledge protocols (ZKP), see [1]. After that course we started to play with unorthodox ideas for breaking ZKP, especially one based on graph 3-coloring. It was chosen for investigation because it is being considered as a "benchmark" ZKP, see [2], [3]. At this point we briefly recall such a protocol's description.


Fast evaluation of union-intersection expressions

Abstract: We show how to represent sets in a linear space data structure such that expressions involving unions and intersections of sets can be computed in a worst-case efficient way. This problem has applications in e.g. information retrieval and database systems. We mainly consider the RAM model of computation, and sets of machine words, but also state our results in the I/O model. On a RAM with word size $w$, a special case of our result is that the intersection of $m$ (preprocessed) sets, containing $n$ elements in total, can be computed in expected time $O(n (\log w)^2 / w + km)$, where $k$ is the number of elements in the intersection. If the first of the two terms dominates, this is a factor $w^{1-o(1)}$ faster than the standard solution of merging sorted lists. We show a cell probe lower bound of time $\Omega(n/(w m \log m)+ (1-\tfrac{\log k}{w}) k)$, meaning that our upper bound is nearly optimal for small $m$. Our algorithm uses a novel combination of approximate set representations and word-level parallelism.


Browsing through 3D representations of unstructured picture collections: an empirical study

Abstract: The paper presents a 3D interactive representation of fairly large picture collections which facilitates browsing through unstructured sets of icons or pictures. Implementation of this representation implies choosing between two visualization strategies: users may either manipulate the view (OV) or be immersed in it (IV). The paper first presents this representation, then describes an empirical study (17 participants) aimed at assessing the utility and usability of each view. Subjective judgements in questionnaires and debriefings were varied: 7 participants preferred the IV view, 4 the OV one, and 6 could not choose between the two. Visual acuity and visual exploration strategies seem to have exerted a greater influence on participants' preferences than task performance or feeling of immersion.


Architecture Optimization of a 3-DOF Translational Parallel Mechanism for Machining Applications, the Orthoglide

Abstract: This paper addresses the architecture optimization of a 3-DOF translational parallel mechanism designed for machining applications. The design optimization is conducted on the basis of a prescribed Cartesian workspace with prescribed kinetostatic performances. The resulting machine, the Orthoglide, features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. A small-scale prototype of the Orthoglide under development is presented at the end of this paper.


Linear Time Algorithms Based on Multilevel Prefix Tree for Finding Shortest Path with Positive Weights and Minimum Spanning Tree in a Networks

Abstract: In this paper I present general outlook on questions relevant to the basic graph algorithms; Finding the Shortest Path with Positive Weights and Minimum Spanning Tree. I will show so far known solution set of basic graph problems and present my own. My solutions to graph problems are characterized by their linear worst-case time complexity. It should be noticed that the algorithms which compute the Shortest Path and Minimum Spanning Tree problems not only analyze the weight of arcs (which is the main and often the only criterion of solution hitherto known algorithms) but also in case of identical path weights they select this path which walks through as few vertices as possible. I have presented algorithms which use priority queue based on multilevel prefix tree -- PTrie. PTrie is a clever combination of the idea of prefix tree -- Trie, the structure of logarithmic time complexity for insert and remove operations, doubly linked list and queues. In C++ I will implement linear worst-case time algorithm computing the Single-Destination Shortest-Paths problem and I will explain its usage.


Multi and Independent Block Approach in Public Cluster

Abstract: We present extended multi block approach in the LIPI Public Cluster. The multi block approach enables a cluster to be divided into several independent blocks which run jobs owned by different users simultaneously. Previously, we have maintained the blocks using single master node for all blocks due to efficiency and resource limitations. Following recent advancements and expansion of node\'s number, we have modified the multi block approach with multiple master nodes, each of them is responsible for a single block. We argue that this approach improves the overall performance significantly, for especially data intensive computational works.


A Neural Networks Model of the Venezuelan Economy

Abstract: Besides an indicator of the GDP, the Central Bank of Venezuela generates the so called Monthly Economic Activity General Indicator. The a priori knowledge of this indicator, which represents and sometimes even anticipates the economy's fluctuations, could be helpful in developing public policies and in investment decision making. The purpose of this study is forecasting the IGAEM through non parametric methods, an approach that has proven effective in a wide variety of problems in economics and finance.


A Non Parametric Study of the Volatility of the Economy as a Country Risk Predictor

Abstract: This paper intends to explain Venezuela's country spread behavior through the Neural Networks analysis of a monthly economic activity general index of economic indicators constructed by the Central Bank of Venezuela, a measure of the shocks affecting country risk of emerging markets and the U.S. short term interest rate. The use of non parametric methods allowed the finding of non linear relationship between these inputs and the country risk. The networks performance was evaluated using the method of excess predictability.


An Early Warning System for Bankruptcy Prediction: lessons from the Venezuelan Bank Crisis

Abstract: During 1993-94 Venezuela experienced a severe banking crisis which ended up with 18 commercial banks intervened by the government. Here we develop an early warning system for detecting credit related bankruptcy through discriminant functions developed on financial and macroeconomic data predating the crisis. A robustness test performed on these functions shows high precision in error estimation. The model calibrated on pre-crisis data could detect abnormal financial tension in the late Banco Capital many months before it was intervened and liquidated.


The Church Synthesis Problem with Parameters

Abstract: For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y=F(X) such that ψ(X,F(X)) is universally valid over Nat. B\"{u}chi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can also be solved by an operator defined by a finite state automaton or equivalently by an MLO formula. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a unary predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of <Nat,<,P> is decidable. We prove that the B\"{u}chi-Landweber theorem can be extended only to ultimately periodic parameters. However, the MLO-definability part of the B\"{u}chi-Landweber theorem holds for the parameterized version of the Church synthesis problem.


Gaze as a Supplementary Modality for Interacting with Ambient Intelligence Environments

Abstract: We present our current research on the implementation of gaze as an efficient and usable pointing modality supplementary to speech, for interacting with augmented objects in our daily environment or large displays, especially immersive virtual reality environments, such as reality centres and caves. We are also addressing issues relating to the use of gaze as the main interaction input modality. We have designed and developed two operational user interfaces: one for providing motor-disabled users with easy gaze-based access to map applications and graphical software; the other for iteratively testing and improving the usability of gaze-contingent displays.


Deciding security properties for cryptographic protocols. Application to key cycles

Abstract: There is a large amount of work dedicated to the formal verification of security protocols. In this paper, we revisit and extend the NP-complete decision procedure for a bounded number of sessions. We use a, now standard, deducibility constraints formalism for modeling security protocols. Our first contribution is to give a simple set of constraint simplification rules, that allows to reduce any deducibility constraint system to a set of solved forms, representing all solutions (within the bound on sessions). As a consequence, we prove that deciding the existence of key cycles is NP-complete for a bounded number of sessions. The problem of key-cycles has been put forward by recent works relating computational and symbolic models. The so-called soundness of the symbolic model requires indeed that no key cycle (e.g., enc(k,k)) ever occurs in the execution of the protocol. Otherwise, stronger security assumptions (such as KDM-security) are required. We show that our decision procedure can also be applied to prove again the decidability of authentication-like properties and the decidability of a significant fragment of protocols with timestamps.


A Polynomial-time Algorithm for Computing the Permanent in GF(3^q)

Abstract: A polynomial-time algorithm for computing the permanent in any field of characteristic 3 is presented in this article. The principal objects utilized for that purpose are the Cauchy and Vandermonde matrices, the discriminant function and their generalizations of various types. Classical theorems on the permanent such as the Binet-Minc identity and Borchadt's formula are widely applied, while a special new technique involving the notion of limit re-defined for fields of finite characteristics and corresponding computational methods was developed in order to deal with a number of polynomial-time reductions. All the constructions preserve a strictly algebraic nature ignoring the structure of the basic field, while applying its infinite extensions for calculating limits. A natural corollary of the polynomial-time computability of the permanent in a field of a characteristic different from 2 is the non-uniform equality between the complexity classes P and NP what is equivalent to RP=NP (Ref. [1]).