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Symbolic and Numeric Algorithms for Scientific Computing, 2007. SYNASC. International Symposium on

Date 26-29 Sept. 2007

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  • Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Cover

    Page(s): c1
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  • Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Title page

    Page(s): i - iii
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  • Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Copyright

    Page(s): iv
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  • Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - TOC

    Page(s): v - x
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  • Preface

    Page(s): xi
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  • Committees

    Page(s): xii - xvi
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  • The Gradual Computerisation of Mathematics in MathLang

    Page(s): 3
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (399 KB) |  | HTML iconHTML  

    The MathLang project aims at computerizing mathematical texts according to various degrees of formalisations, and without any prior commitment to a particular logical framework or to a particular proof checker. In this paper, the MathLang framework, its developments and its current and future aspects, as well as examples of computerization from original mathematical texts to the fully formalised Mizar versions are given. For each aspect, emphasis will be on its design, formalisation, implementation, the automation available for this aspect and the correctness or trustworthiness of these processes. Then, we discuss how the computerisation path from the original mathematical text to full Mizar will look if Isabelle was the checker chosen instead of Mizar and show that a number of aspects and computerised versions of the original text are common between both path. We also discuss at which stage a commitment to a certain logical framework and a certain proof checker can be made on the path from the original mathematical text to the version fully formalised in that proof checker. View full abstract»

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  • SymGrid: A Framework for Symbolic Computations on the Grid

    Page(s): 4
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (398 KB) |  | HTML iconHTML  

    Summary form only given. As part of a major EU infrastructure project (SCIEnce: Symbolic Computing Infrastructure in Europe), we are developing SymGrid, a new framework that will, for the first time, allow multiple invocations of symbolic computing applications to interact via the Grid. SymGrid is designed to support the specific needs of symbolic computation, including computational steering (greater interactivity), complex data structures, and domain-specifc computational patterns (for irregular parallelism). A key issue for the SymGrid design is heterogeneity: SymGrid is designed to orchestrate legacy components from different symbolic systems into a single coherent (possibly parallel) Grid application, building on the OpenMath standard for data exchange between mathematically-oriented applications. View full abstract»

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  • Relational Declarative Programming with JBoss Drools

    Page(s): 5
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    Summary form only given. This talk will focus on declarative programming with JBoss Drools 4.0. We will cover all of the advanced Conditional Elements that facilitate declarative programming; including 'exists, 'not', 'collect', 'accumulate' and 'from'. We will discuss why object models should be flattened and expressed relationally to get the most out of declarative programming with rule engines. The new Ruleflow extensions will be covered and why an integrated engine for rules and process is essential for complex behavioral modeling. The future of Drools will also be touched on and our possible approaches to integrate CEP/ESP, backward chaining, solvers and belief systems. This talk will be aimed at intermediates and above, it is expected that attendees should understand the basics on Production Rule systems; and how assertion and retraction on a rule session work along with the role of the agenda and the recursive nature of rule systems. View full abstract»

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  • P2P Open Agent Networks for Decision Making

    Page(s): 6
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (401 KB) |  | HTML iconHTML  

    Peer-to-peer (P2P) computing, a recently developed network architecture for distributed systems, is currently receiving ever increasing attention of both academia and industry. It has become a driving force for many new ideas and opportunities in design and implementation of modern large scale applications composed of highly autonomous entities. Recent efforts intended to integrate multi-agent, service-orients and P2P architectures aim to make these very promising opportunities happen. View full abstract»

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  • Some Applications of Weakly Picard Operators

    Page(s): 7 - 10
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    In this paper we present some notions and results from the weakly Picard operator theory. Applications to iterates of linear operators are given. Some open problems are also discussed. View full abstract»

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  • Journal as Active Math-Agents: Outline of a Project with a Mathematics Publisher

    Page(s): 11 - 12
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (406 KB) |  | HTML iconHTML  

    As in any other scientific field, the quality control (by peer reviewing), archiving and distribution of knowledge in mathematics is organized by journals. Currently, mathematical journals represent huge chunks of knowledge that sit passively on a shelf and wait for a human user to read or query them. In contrast, what we want to achieve in this project is the transformation of the knowledge contained in mathematical journals into formal mathematical knowledge bases that behave as active reasoning agents. View full abstract»

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  • Modeling Origami and Beyond

    Page(s): 13
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (414 KB) |  | HTML iconHTML  

    We discuss some aspects of the computational origami as a new kind of science of shapes. The computational origami is closely linked to paper craft, traditional art, industrial art, geometry of all levels, and furthermore to computer science. In this talk we present models of origami for computer assisted construction of and reasoning about origami. View full abstract»

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  • 'Descente Infinie' Induction-Based Saturation Procedures

    Page(s): 17 - 24
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB) |  | HTML iconHTML  

    In [11], we have shown that implicit induction and saturation proof techniques share the same logic, witnessed by an inference system implementing the Fermat's 'Descente Infinie' induction principle. As a case study, a simple paramodulation-based inference system has been proved as an instance of it. In this paper, we detail the instantiation method to treat general saturation-based systems and apply it to analyse a non-trivial resolution-based system. We also propose a methodology to build variants of existing systems, which preserve crucial properties like soundness and refutational completeness. View full abstract»

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  • A Tool for Calculating Exponential Run-Time Properties

    Page(s): 25 - 32
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (622 KB) |  | HTML iconHTML  

    Affine size-change analysis has been used for calculating precise polynomial bounds on the run times, and stack depths of affine size-change terminating programs. Such polynomial costs may be discovered by a characterization as a problem in quantifier elimination. In this paper we extend this work to cover a class of exponential cost programs. The tool described allows the calculation of run-time and stack-depth costs for some classes of exponential-cost programs, again by using quantifier elimination. The technique is automated, and uses the reduce computer algebra system. View full abstract»

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  • Strategy-Based and Knowledge-Based Models of Information Flow: Equivalence and Decidability

    Page(s): 33 - 40
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (211 KB) |  | HTML iconHTML  

    We show that two notions of information flow, one which is strategy-based and the other knowledge-based, are equivalent. The first notion models the possibilities that a high-level user has to send information to the low-level user by distinctly observable runs, whereas the second notion models information leak as variations in the knowledge of the low-level user during his observation of the system behavior. We also give an algorithm for deciding whether a finite-state system has no information flow in our setting, by reducing the problem to a reachability problem in finite automata. View full abstract»

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  • Decompositions of Natural Numbers: From a Case Study in Mathematical Theory Exploration

    Page(s): 41 - 47
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (525 KB) |  | HTML iconHTML  

    In the context of a scheme based exploration model proposed by Bruno Buchberger, we investigate the idea of decomposition, applied in the exploration of natural numbers. The free decomposition problem (i.e. whether an element can always be decomposed with respect to an operation) can be arbitrarily difficult, and we illustrate this in the theory of natural numbers. We consider a restriction, the decomposition in domains with a well-founded partial ordering: we introduce the notions of irreducible elements, reducible elements w.r.t. a composition operation, decomposition of domain elements into irreducible ones, and also the problem of irreducible decomposition which we then solve. Natural numbers can be classified as a decomposition domain, in which we know how to solve the decomposition problem. This leads to the prime decomposition theorem. View full abstract»

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  • Functional-Based Comparison between Two Special Classes of Uni- and Bidirectional Systolic Arrays

    Page(s): 51 - 58
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (583 KB) |  | HTML iconHTML  

    In this paper we compare two special classes of systolic arrays, namely unidirectional systolic arrays with delayed output and bidirectional systolic arrays with one directional pass-through input. We make use of the results of [5], where we presented a so called functional approach to the synthesis of unidirectional arrays. By analysing the behaviour of arrays with two directional data-flow we determine the conditions and the cases in which the two corresponding (uni- and bidirectional) array types are solving the same class of problems. Thus the synthesis problem for the two different array types can be solved simultaneously. View full abstract»

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  • Parallel Multiple Polynomial Quadratic Sieve on Multi-Core Architectures

    Page(s): 59 - 65
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (576 KB) |  | HTML iconHTML  

    The ability of multi-core processors to increase application performance depends on the use of multiple threads within applications. Symbolic computations, requiring both CPU power and large memory, are well-suited candidates for deriving advantages from multi-core parallel architectures. This is possible only if the specific libraries and tools are designed to allow multi-threading and multi-processes. In order to promote the changes needed to adapt these libraries and tools to the new architectures, the changes performed of a main algorithm for symbolic computations, parallel integer factorization, is described and discussed. View full abstract»

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  • Branching Programs, Grammar Systems and the NC1 Class

    Page(s): 66 - 73
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (585 KB) |  | HTML iconHTML  

    Cooperating distributed grammar systems (CDGSs) are sets of Chomsky grammars that work sequentially on a common sentential form according to a specified protocol of cooperation. Branching programs (BPs) are fundamental models of non-uniform computation that simultaneously capture time and space in sequential computation. In this paper we deal with simulations of CDGSs by bounded width branching programs (BWBPs). We present several lower and upper bounds for time, space and cooperation (communication) complexity measures for CDGSs that emerge from these simulations. It is widely known that the class of languages recognizable by BWBPs equals the NC1 class, i.e., the class of languages recognizable by fan-in two, logarithmic-depth and polynomial-size uniform Boolean circuits. With respect to this result and the simulations presented in this paper, the class of the Szilard languages associated to derivations in CDGSs are related to the NC1 class. View full abstract»

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  • Structural Properties and Observability in Membrane Systems

    Page(s): 74 - 81
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (869 KB) |  | HTML iconHTML  

    We assimilate some notions of the ambient calculus into the formalism of membrane systems. Thus we consider the exhibit of an ambient, its level, the structural congruence, and the contextual bisimulation to define and study in mobile membrane systems the corresponding observation barbs, the depths of a membrane system, and the structural congruence. The relation between these notions is given by a translation function. View full abstract»

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  • Proving Behavioral Commutativity with CIRC

    Page(s): 85 - 92
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (543 KB) |  | HTML iconHTML  

    CIRC is an automated circular coinductive prover implemented as an extension of Maude. In this paper we extend CIRC with the capability to prove behavioral commutativity and we show that the method is sound. The strength of the extended version of CIRC is illustrated on the example of coinductive calculus of streams. View full abstract»

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  • Identification of Relational Discrepancies between Database Schemas and Source-Code in Enterprise Applications

    Page(s): 93 - 100
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (972 KB) |  | HTML iconHTML  

    As enterprise applications become more and more complex, the understanding and quality assurance of these systems become an increasingly important issue. One specific concern of data reverse engineering, a necessary process for this type of applications which tackles the mentioned aspects, is to retrieve constraints which are not explicitly declared in the database schema but verified in the code. In this paper we propose a novel approach for detecting the relational discrepancies between database schemas and source-code in enterprise applications, as part of the data reverse engineering process. Detecting and removing these discrepancies allows us to ensure the accuracy of the stored data as well as to increase the level of understanding of the data involved in an enterprise application. View full abstract»

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  • McC and Mc#: Unified C++ and C# Design Facts Extractors Tools

    Page(s): 101 - 104
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (606 KB) |  | HTML iconHTML  

    In the last years, as object-oriented software systems have become more and more complex, the need of performing automatically reverse engineering upon such systems has significantly increased. It is well known that one step toward a research infrastructure accelerating the progress of reverse engineering is the creation of an intermediate representation of software systems. In the current demonstration we present an unified structure for representing object- oriented systems written in C++ and C#, together with the corresponding model capturing tools. As a result, we can uniformly analyze C++ and C# systems. Moreover, we have integrated the tools in the iPlasma reengineering infrastructure which permits us to obtain easily valuable information for a reverse engineering process. View full abstract»

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  • Sharing Rules between JBoss and Jena

    Page(s): 105 - 108
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (448 KB) |  | HTML iconHTML  

    The actual rule based implementations point to different rule target platforms and languages (object oriented rule languages, semantic Web rule languages, artificial intelligence rule languages) in a business landscape dominated by a limited number of tool vendors as well as competitive open-source platforms and rule interoperability initiatives. This work provides a description of business rules translation from JBoss-Rules - an object oriented rule-system, to Jena Rules - a semantic Web rule-system, via an interchange language. It focuses on the general lines of the JBoss- RZML-Jena translation and to outline the limitations and on the correctness of the proposed interchange. View full abstract»

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