A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations

Yohan Boichut (1) , Pierre-Cyrille Heam (2)

1 PAREO - Formal islands: foundations and applications
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

In computer aided verification, the reachability problem is particularly relevant for safety analyses. Given a regular tree language L, a term t and a relation R, the reachability problem consists in deciding whether a sequence of terms, beginning with a term of L and terminating on t and such that two successive terms of this sequence are in relation according to R, is constructable. In this case, the term t is said to be reachable, otherwise it is said unreachable. This problem is decidable for particular kinds of relations, but it is known to be undecidable in general, even if L is finite. Several approaches to tackle the unreachability problem are based on the computation of an R-closed regular language containing L. In this paper we show a theoretical limit to this kind of approaches for this problem.

Mots clés: reachability problem; regular tree languages; undecidable; theoretical limit

Domaines: Autre [cs.OH]

Yohan Boichut, Pierre-Cyrille Heam. A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations. [Research Report] RR-6411, INRIA. 2008, pp.6. ⟨inria-00204579v2⟩