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Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2009 11th International Symposium on

Date 26-29 Sept. 2009

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  • [Front cover]

    Publication Year: 2009, Page(s): C1
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  • [Title page i]

    Publication Year: 2009, Page(s): i
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  • [Title page iii]

    Publication Year: 2009, Page(s): iii
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  • [Copyright notice]

    Publication Year: 2009, Page(s): iv
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  • Table of contents

    Publication Year: 2009, Page(s):v - ix
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  • Preface

    Publication Year: 2009, Page(s):x - xi
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  • Conference Committees

    Publication Year: 2009, Page(s):xii - xiv
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  • list-reviewer

    Publication Year: 2009, Page(s): xv
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  • The Sparsity Challenges

    Publication Year: 2009, Page(s):3 - 7
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (178 KB) | HTML iconHTML

    While much is written about the importance of sparse polynomials in computer algebra, much less is known about the complexity of advanced (i.e. anything more than multiplication!) algorithms for them. This is due to a variety of factors, not least the problems posed by cyclotomic polynomials. In this paper we state a few of the challenges that sparse polynomials pose. View full abstract»

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  • Coloring Random Graphs: A Short Survey

    Publication Year: 2009, Page(s): 8
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (97 KB) | HTML iconHTML

    We shortly present some recent results concerning the chromatic number of random graphs. The setting is as follows: we consider a probability space with graphs of a given average degree d and n vertices (the term "average" here refers to the ratio of the sum of the degrees of all vertices to n). In the first case (the Erd¿s-Renyi graphs), the probability space comprises all graphs with average de... View full abstract»

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  • A Compiler for Origami Construction and Verification

    Publication Year: 2009, Page(s): 9
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (107 KB) | HTML iconHTML

    This is the extended abstract of the invited tutorial on a compiler for origami construction and verification. View full abstract»

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  • Finding Loop Invariants for Programs over Arrays Using a Theorem Prover

    Publication Year: 2009, Page(s): 10
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (102 KB) | HTML iconHTML

    Invariants with quantifiers are important for verification and static analysis of programs over arrays due to the unbounded nature of arrays. Such invariants can express relationships among array elements and properties involving array and scalar variables of the loop. This talk presents how quantified loop invariants of programs over arrays can be automatically inferred using a first order theore... View full abstract»

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  • Embedding Formal Methods into Systems Engineering

    Publication Year: 2009, Page(s): 11
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (114 KB)

    'Summary form only given.' Industrial computing is rapidly moving towards systems that exhibit vast amounts of internal concurrency and communication, most visibly in many-core architectures, but equally important in the MilliWatt scale of embedded systems and the GigaWatt scale of cloud computing. The shift of focus from stand-alone systems connected through a network to collaborative computation... View full abstract»

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  • SMT Solvers for Testing, Program Analysis and Verification at Microsoft

    Publication Year: 2009, Page(s): 15
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (112 KB) | HTML iconHTML

    Modern program analysis and model-based tools are increasingly complex and multi-faceted software systems. However, at their core is invariably a component using logic for describing states and transformations between system states. The system Z3, developed at Microsoft Research, is a Satisfiability Modulo Theories (SMT) solver. It provides logic inference capabilities that are critical for the fu... View full abstract»

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  • Satisfiability and Theories

    Publication Year: 2009, Page(s): 16
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (92 KB)

    Summary form only given. We give a simple introduction to satisfiability modulo theories intended for non-specialists. No previous background is assumed. The tutorial covers the following topics. 1) Propositional satisfiability. 2) DPLL as the main method for satisfiability checking. 3) Implementations of DPLL. 4) Theories. 5) Decision procedures for theories. Congruence closure, the theory of arr... View full abstract»

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  • Automated Methods for Proving Program Termination and Liveness

    Publication Year: 2009, Page(s): 17
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (135 KB) | HTML iconHTML

    Proving program termination is an important step towards ensuring software reliability. The programmers expect that the majority of code fragments, including procedures, event handles, or other program components, always terminates. Unfortunately, until recently there were no viable approaches for automatically proving termination of programs written in imperative programming languages. View full abstract»

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  • Automated Software Analysis

    Publication Year: 2009, Page(s): 18
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (128 KB) | HTML iconHTML

    Recent years have seen tremendous progress in the capabilities of software model checkers. These tools are the result of combined efforts by different communities, most notably model checking, abstract interpretation, program semantics, and decision procedures. In this tutorial, we will introduce the fundamentals of software model checking, and show how the different origins of the field combine t... View full abstract»

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  • m-Hilbert Polynomial and Arbitrariness of the General Solution of Partial Differential Equations

    Publication Year: 2009, Page(s):21 - 27
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (229 KB) | HTML iconHTML

    Using the framework of formal theory of partial differential equations, we consider a method of computation of the m-Hilbert polynomial (i.e. Hilbert polynomial with multivariable), which generalizes the Seiler's theorem of Hilbert polynomial with single variable. Next we present an approach to compute the number of arbitrary functions of positive differential order in the general solution, and gi... View full abstract»

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  • Computing Self-intersection Loci of Parametrized Surfaces Using Regular Systems and Groebner Bases

    Publication Year: 2009, Page(s):28 - 36
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (264 KB) | HTML iconHTML

    The computation of self-intersection loci of parametrized surfaces is needed for constructing trimmed parametrizations and describing the topology of the considered surfaces in real settings. This paper presents two general and efficient methods for determining self-intersection loci of rationally parametrized surfaces. One of the methods, based on regular systems, is capable of computing the exac... View full abstract»

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  • A Hybrid Algorithm for Solving 7 Parameters Transformation

    Publication Year: 2009, Page(s):37 - 44
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (316 KB) | HTML iconHTML

    The 7 parameters transformation is a well-known problem in engineering sciences such as Computer Vision, Survey Engineering and Photogrammetry. To solve this problem, we use an algebraic solver in which we need to transform the input system into an equivalent system, but better adapted such as a Gro¿bner basis. For operational applications of this problem, we need to compute this basis as fast as... View full abstract»

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  • Superfluous S-polynomials in Strategy-Independent Groebner Bases

    Publication Year: 2009, Page(s):45 - 53
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (228 KB) | HTML iconHTML

    Using the machinery of proof orders originally introduced by Bachmair and Dershowitz in the context of canonical equational proofs, we give an abstract, strategy-independent presentation of Groebner basis procedures and prove the correctness of two classical criteria for recognising superfluous S-polynomials, Buchberger's criteria 1 and 2, w.r.t. arbitrary fair and correct basis construction strat... View full abstract»

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  • Toom-Cook 8-way for Long Integers Multiplication

    Publication Year: 2009, Page(s):54 - 57
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (252 KB) | HTML iconHTML

    Toom-Cook algorithms are efficient subquadratic polynomial/long integers multiplication methods. In general, only the degree 2 (Karatsuba), 3 and 4 version are used in practice. In this paper we analyse a high (8-way - degree 7) version, showing it can be effective for long integers whose digits number lies in a certain range. Comparison with GMP 4.3.0 library shows that the gain for multiplicatio... View full abstract»

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  • A Hierarchy of Tractable Subclasses for SAT and Counting SAT Problems

    Publication Year: 2009, Page(s):61 - 68
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (215 KB) | HTML iconHTML

    Finding subclasses of formulae for which the SAT problem can be solved in polynomial time has been an important problem in computer science. We present a new hierarchy of propositional formulÿ subclasses for which the SAT and counting SAT problems can be solved in polynomial time. Our tractable subclasses are those propositional formulae in conjunctive normal form where any set of k + 1 clauses a... View full abstract»

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  • Formal Proof of Theorems on Genetic Regulatory Networks

    Publication Year: 2009, Page(s):69 - 76
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    We describe the formal verification of two theorems of theoretical biology. These theorems concern genetic regulatory networks: they give, in a discrete modeling framework, relations between the topology and the dynamics of these biological networks. In the considered discrete modeling framework, the dynamics is described by a transition graph, where vertices are vectors indicating the expression ... View full abstract»

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  • A Calculus for Imperative Programs: Formalization and Implementation

    Publication Year: 2009, Page(s):77 - 84
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (202 KB) | HTML iconHTML

    As an extension of our previous work on imperative program verification, we present a formalism for handling the total correctness of While loops in imperative programs, consisting in functional based definitions of the verification conditions for both partial correctness and for termination.A specific feature of our approach is the generation of verification conditions as first order formulae, in... View full abstract»

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