Finitely Representing Infinite Reachability Graphs of CFSMs with Graph Grammars

We propose here an algorithm enabling to represent, in a finite way, some infinite reachability graphs of communicating finite-state machines, by using a graph grammar. The model-checking algorithm presented in Burkart and Quemener (1996) uses that finite representation for verifying properties of the infinite graph. In way to obtain that finite representation, we use a result of Jeron and Jard (1993): it can be detected that some sequences of transitions are infinitely repeated. We show here that the transitions issued from states linked by such sequences are also infinitely repeated if they are repeated twice. We deduce a method for detecting patterns that compose the infinite reachability graph on study.

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