Continuous One-counter Automata-Reference-Cited by-同舟云学术

Continuous One-counter Automata

Published:2023-01-18 Issue:1 Volume:24 Page:1-31
ISSN:1529-3785
Container-title:ACM Transactions on Computational Logic
language:en
Short-container-title:ACM Trans. Comput. Logic

Author:

Blondin Michael¹^ORCID,Leys Tim²^ORCID,Mazowiecki Filip³^ORCID,Offtermatt Philip⁴^ORCID,Pérez Guillermo⁵^ORCID

Affiliation:

1. Université de Sherbrooke, Sherbrooke, Québec, Canada

2. University of Antwerp, Antwerpen, Belgium

3. Max Planck Institute for Software Systems, Saarbrücken, Saarland, Germany

4. Université de Sherbrooke;, Sherbrooke, Québec, Canada, and Max Planck Institute for Software Systems, Saarbrücken, Saarland, Germany

5. University of Antwerp – Flanders Make, Antwerpen, Belgium

Abstract

We study the reachability problem for continuous one-counter automata, COCA for short. In such automata, transitions are guarded by upper- and lower-bound tests against the counter value. Additionally, the counter updates associated with taking transitions can be (non-deterministically) scaled down by a nonzero factor between zero and one. Our three main results are as follows: we prove (1) that the reachability problem for COCA with global upper- and lower-bound tests is in NC 2 ; (2) that, in general, the problem is decidable in polynomial time; and (3) that it is NP-complete for COCA with parametric counter updates and bound tests.

Funder

Natural Sciences and Engineering Research Council of Canada

Research Foundation – Flanders

Publisher

Association for Computing Machinery (ACM)

Subject

Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/3558549

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5. Continuous One-Counter Automata