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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Flat Parametric Counter Automata
verfasst von : Marius Bozga, Radu Iosif, Yassine Lakhnech
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
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In this paper we study the reachability problem for parametric flat counter automata, in relation with the satisfiability problem of three fragments of integer arithmetic. The equivalence between non-parametric flat counter automata and Presburger arithmetic has been established previously by Comon and Jurski [5]. We simplify their proof by introducing finite state automata defined over alphabets of a special kind of graphs (zigzags). This framework allows one to express also the reachability problem for parametric automata with one control loop as the existence of solutions of a
1-parametric linear Diophantine systems
. The latter problem is shown to be decidable, using a number-theoretic argument. Finally, the general reachability problem for parametric flat counter automata with more than one loops is shown to be undecidable, by reduction from Hilbert’s Tenth Problem [9].