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

Abstract : 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.
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Contributor : Grégoire Sutre <>
Submitted on : Thursday, December 20, 2018 - 3:32:35 PM
Last modification on : Friday, February 26, 2021 - 11:31:27 AM
Long-term archiving on: : Friday, March 22, 2019 - 11:09:49 AM


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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-01848554v2⟩



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