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Convex Hull of Arithmetic Automata

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Static Analysis (SAS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5079))

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Abstract

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata.

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Authors and Affiliations

  1. LaBRI, Université de Bordeaux, CNRS, Domaine Universitaire, 351, cours de la Libération, 33405, Talence, France

    Jérôme Leroux

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  1. Jérôme Leroux
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María Alpuente Germán Vidal

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Leroux, J. (2008). Convex Hull of Arithmetic Automata. In: Alpuente, M., Vidal, G. (eds) Static Analysis. SAS 2008. Lecture Notes in Computer Science, vol 5079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69166-2_4

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  • DOI: https://doi.org/10.1007/978-3-540-69166-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69163-1

  • Online ISBN: 978-3-540-69166-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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