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Multiple counters automata, safety analysis and Presburger arithmetic (1998)
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BibTeX
@MISC{Comon98multiplecounters,
author = {Hubert Comon and Y. Jurski},
title = {Multiple counters automata, safety analysis and Presburger arithmetic},
year = {1998}
}
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Abstract
We consider automata with counters whose values are updated according to signals sent by the environment. A transition can be fired only if the values of the counters satisfy some guards (the guards of the transition). We consider guards of the form y i #y j +c i;j where y i is either x 0 i or x i , the values of the counter i respectively after and before the transition, and # is any relational symbol in f=; ; ; ?; !g. We show that the set of possible counter values which can be reached after any number of iterations of a loop is definable in the additive theory of N (or Z or R depending on the type of the counters). This result can be used for the safety analysis of multiple counters automata.
