Reachability for Two-Counter Machines with One Test and One Reset

Alain Finkel (1) , Jérôme Leroux (2) , Grégoire Sutre (2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We prove that the reachability relation of two-counter machines with one zero-test and one reset is Presburger-definable and effectively computable. Our proof is based on the introduction of two classes of Presburger-definable relations effectively stable by transitive closure. This approach generalizes and simplifies the existing different proofs and it solves an open problem introduced by Finkel and Sutre in 2000.

Mots clés: Infinite-state system; Formal verification; Presburger arithmetic; Counter machine; Vector addition system; Reachability problem

Domaines: Théorie et langage formel [cs.FL]; Logique en informatique [cs.LO]

Alain Finkel, Jérôme Leroux, Grégoire Sutre. Reachability for Two-Counter Machines with One Test and One Reset. FSTTCS 2018 - 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Dec 2018, Ahmedabad, India. pp.31:1-31:14, ⟨10.4230/LIPIcs.FSTTCS.2018.31⟩. ⟨hal-01848554v1⟩