On (Omega-)regular model checking

Abstract

Checking infinite-state systems is frequently done by encoding infinite sets of states as regular languages. Computing such a regular representation of, say, the set of reachable states of a system requires acceleration techniques that can finitely compute the effect of an unbounded number of transitions. Among the acceleration techniques that have been proposed, one finds both specific and generic techniques. Specific techniques exploit the particular type of system being analyzed, e.g. a system manipulating queues or integers, whereas generic techniques only assume that the transition relation is represented by a finite-state transducer, which has to be iterated. In this paper, we investigate the possibility of using generic techniques in cases where only specific techniques have been exploited so far. Finding that existing generic techniques are often not applicable in cases easily handled by specific techniques, we have developed a new approach to iterating transducers. This new approach builds on earlier work, but exploits a number of new conceptual and algorithmic ideas, often induced with the help of experiments, that give it a broad scope, as well as good performances.

Extrapolating (omega-)regular model checking

“…The following proposition, which is taken from [59,61], formalizes the extrapolation procedure. Proof Let δ be the transition relation of A e 0 .…”

“…In [27,28,61], we have proposed a generic sufficient criterion for checking the precision of the extrapolation. The check builds on counters that are added during the extrapolation process and used to prove the precision property in an inductive manner.…”

“…The problem can easily be solved by duplicating the head increment. This is illustrated with the following proposition taken from [59,61]. Proof Let δ be the transition relation of A e 0 .…”

“…In Table 1, we give the number of states of the minimal and deterministic form of the automaton A S 0 representing the initial set of states, of the transducer T representing the reachability relation, of the largest power T i (A S 0 ) that was constructed, and of the set of reachable states T * (A S 0 ). We denote by T1(s) the time needed to compute a safe extrapolation of the set of reachable states, and by T2(s) the time needed to compute a safe extrapolation and to assess its precision with the check of [61]. …”

“…Most of the computation time was 136 A. Legay , y), (x + 2, y − 1))}∪ x, y, z), (w + 1, x + 2, y + 3, z + 4))} 91 1,500 251 11.7 1 6 .5 Table 4 Examples of transducers and their iteration Relation consumed when computing the successive automata to build the incrementally growing sampling sequence but not by the extrapolation technique which lasted for a few seconds. We tried to establish the precision of the extrapolations using the extrapolation counter-based approach of [61], but we were unable to manage the intermediate structures required by the algorithms. 9 We suspect that is related to the need of combining two different encodings for integer variable values: the binary encoding of [82] for the variables of the relation and the encoding of the counters involved in the precision check.…”