Iterating Octagons

Marius Bozga (1) , Codruta Girlea (1) , Radu Iosif (1)

1 VERIMAG - IMAG - VERIMAG

In this paper we prove that the transitive closure of a non-deterministic octagonal relation using integer counters can be expressed in Presburger arithmetic. The direct consequence of this fact is that the reachability problem is decidable for flat counter automata with octagonal transition relations. This result improves the previous results of Comon and Jurski, and Bozga, Iosif and Lakhnech concerning the computation of transitive closures for difference bound relations. The importance of this result is justified by the wide use of octagons to computing sound abstractions of real-life systems. We have implemented the octagonal transitive closure algorithm in a prototype system for the analysis of counter automata, called FLATA, and we have experimented with a number of test cases.

Mots clés: difference bound relations; octagonal relations; tranzitive closure; Presburger arithmetic

Domaines: Systèmes embarqués

Marius Bozga, Codruta Girlea, Radu Iosif. Iterating Octagons. Tools and Algorithms for the Construction and Analysis of Systems 15th International Conference, TACAS 2009, Mar 2009, York, United Kingdom. pp.337-351, ⟨10.1007/978-3-642-00768-2⟩. ⟨hal-00374863⟩