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Global and local invariants in transition systems

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Book cover Automata, Languages and Programming (ICALP 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 140))

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Abstract

Given a transition system and a cover P of the set of its states, a set of local invariants with respect to P is defined as a set of predicates in bijection with the blocks of P and in such a way that a local invariant be true every time the system is in a state belonging to the corresponding block of the cover.

This definition is proved to be sufficiently general in the sense that any proof made by using global invariants can be also made by using sets of local invariants. The same result is proved for two more restrictive definitions of the notion of local invariant by using well-known properties of connections between lattices.

Finally, it is shown how the theory of connections can provide a general frame for tackling the problem of decomposing a global assertion into a logically equivalent set of local assertions.

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Authors and Affiliations

  1. IMAG, BP53X, 38041, Grenoble Cedex, France

    Joseph Sifakis

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  1. Joseph Sifakis
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Mogens Nielsen Erik Meineche Schmidt

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© 1982 Springer-Verlag Berlin Heidelberg

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Sifakis, J. (1982). Global and local invariants in transition systems. In: Nielsen, M., Schmidt, E.M. (eds) Automata, Languages and Programming. ICALP 1982. Lecture Notes in Computer Science, vol 140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012796

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  • DOI: https://doi.org/10.1007/BFb0012796

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11576-2

  • Online ISBN: 978-3-540-39308-5

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