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On the analysis and synthesis of free choice systems

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Advances in Petri Nets 1990 (ICATPN 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 483))

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Abstract

This invited paper present in a semi-formal illustrative way several new results concerning the analysis and synthesis of free choice systems. It is a complementary work of the survey by E. Best [Best 87]. In the analysis part, we characterize liveness and boundedness in linear algebraic terms. As a consequence of the new characterizations, both properties are shown to be decidable (as a whole) in polynomial time. We also provide two different kits of sound and complete reduction rules (the one reverse-dual of the other).

We address then the problem of synthezising live and bounded free choice systems within the two basic design methodologies: top-down and modular (synthesis by composition of modules). Two complete kits of top-down synthesis rules are provided. They are essentially the reduction kits obtained before, but this time considered in the reverse direction. The completeness of the kits can be used to prove new results (or give new proofs of old results) using structural induction on the chain of applications of the rules that synthezise a given system. In the modular approach, exact conditions for the preservation of liveness and boundednes under compositions of systems are given. These conditions are the absence of certain design errors, called killing choices, killing joints, synchronic mismatches and state mismatches. They help to understand why a certain system is not well behaved.

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Authors and Affiliations

  1. Institut für Informatik, Universität Hildesheim, Samelsonplatz 1, D-3200, Hildesheim, Germany

    Javier Esparza

  2. Depto. Ingeniería Eléctrica e Informática, Universidad de Zaragoza, C/María de Luna 3, 50015, Zaragoza, Spain

    Manuel Silva

Authors
  1. Javier Esparza
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  2. Manuel Silva
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Grzegorz Rozenberg

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© 1991 Springer-Verlag Berlin Heidelberg

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Esparza, J., Silva, M. (1991). On the analysis and synthesis of free choice systems. In: Rozenberg, G. (eds) Advances in Petri Nets 1990. ICATPN 1989. Lecture Notes in Computer Science, vol 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53863-1_28

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  • DOI: https://doi.org/10.1007/3-540-53863-1_28

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  • Print ISBN: 978-3-540-53863-9

  • Online ISBN: 978-3-540-46369-6

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