Algorithmic analysis of termination and counter complexity in vector addition systems with states

Author:

Kučera Antonín1

Affiliation:

1. Masaryk University, Czechia

Abstract

We give an overview of recently established results about the effective asymptotic analysis of termination and counter complexity of VASS computations. In contrast to "classical" problems such as reachability, boundedness, liveness, coverability, etc., that are EXPSPACE-hard, the decision problems related to VASS asymptotic analysis tend to have low complexity and many important variants are even decidable in polynomial time. We also present selected concepts and techniques used to achieve these results.

Publisher

Association for Computing Machinery (ACM)

Subject

General Earth and Planetary Sciences,General Environmental Science

Reference19 articles.

1. Deciding Polynomial Termination Complexity for VASS Programs. In Proceedings of CONCUR 2021 (Leibniz International Proceedings in Informatics), Vol. 203;Ajdarów M.;Schloss Dagstuhl-Leibniz-Zentrum für Informatik,2021

2. T. Brázdil , K. Chatterjee , A. Kučera , P. Novotný , and D. Velan . 2019 . Deciding Fast Termination for Probabilistic VASS with Nondeterminism. In Proceedings of ATVA 2019 (Lecture Notes in Computer Science) , Vol. 11781 . Springer , 462 - 478 . T. Brázdil, K. Chatterjee, A. Kučera, P. Novotný, and D. Velan. 2019. Deciding Fast Termination for Probabilistic VASS with Nondeterminism. In Proceedings of ATVA 2019 (Lecture Notes in Computer Science), Vol. 11781. Springer, 462-478.

3. T. Brázdil , K. Chatterjee , A. Kučera , P. Novotný , D. Velan , and F. Zuleger . 2018. Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS . In Proceedings of LICS 2018 . ACM Press , 185 - 194 . T. Brázdil, K. Chatterjee, A. Kučera, P. Novotný, D. Velan, and F. Zuleger. 2018. Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS. In Proceedings of LICS 2018. ACM Press, 185-194.

4. T. Brázdil , P. Jančar , and A. Kučera . 2010. Reachability Games on Extended Vector Addition Systems with States . In Proceedings of ICALP 2010 , Part II (Lecture Notes in Computer Science) , Vol. 6199 . Springer, 478 - 489 . T. Brázdil, P. Jančar, and A. Kučera. 2010. Reachability Games on Extended Vector Addition Systems with States. In Proceedings of ICALP 2010, Part II (Lecture Notes in Computer Science), Vol. 6199. Springer, 478-489.

5. M. Broy and M. Wirsing . 1981. On the Algebraic Specification of Nondeterministic Programming Languages . In Proceedings of CAAP'81 (Lecture Notes in Computer Science) , Vol. 112 . Springer , 162 - 179 . M. Broy and M. Wirsing. 1981. On the Algebraic Specification of Nondeterministic Programming Languages. In Proceedings of CAAP'81 (Lecture Notes in Computer Science), Vol. 112. Springer, 162-179.

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