Flat Counter Automata Almost Everywhere!

Jérôme Leroux (1) , Grégoire Sutre (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be “replaced”, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semi-algorithmic technique implemented in successful tools like Fast, Lash or TReX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflict-free Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a uniform accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass).

Domaines: Algorithme et structure de données [cs.DS]

Jérôme Leroux, Grégoire Sutre. Flat Counter Automata Almost Everywhere!. Third International Symposium, ATVA 2005, 2005, Taipei, Taiwan. pp.489-503, ⟨10.1007/11562948_36⟩. ⟨hal-00346310⟩