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The reachability problem for Petri nets is not elementary
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Czerwiński, Wojciech, Lasota, Sławomir, Lazic, Ranko, Leroux, Jerome and Mazowiecki, Filip (2019) The reachability problem for Petri nets is not elementary. In: STOC 2019, Phoenix, AZ, USA, 23-26 Jun 2019. Published in: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing pp. 24-33. ISBN 9781450367059. doi:10.1145/3313276.3316369
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WRAP-reachability-problem-Petri-nets-not-elementary-Lazic-2019.pdf - Accepted Version - Requires a PDF viewer. Download (1153Kb) | Preview |
Official URL: http://dx.doi.org/10.1145/3313276.3316369
Abstract
Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.
| Item Type: | Conference Item (Paper) | |||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | |||||||||||||||||||||
| Divisions: | Faculty of Science > Computer Science | |||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Petri nets, Computable functions | |||||||||||||||||||||
| Journal or Publication Title: | Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing | |||||||||||||||||||||
| Publisher: | ACM | |||||||||||||||||||||
| ISBN: | 9781450367059 | |||||||||||||||||||||
| Book Title: | Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019 | |||||||||||||||||||||
| Official Date: | 2019 | |||||||||||||||||||||
| Dates: |
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| Date of first compliant deposit: | 23 July 2019 | |||||||||||||||||||||
| Page Range: | pp. 24-33 | |||||||||||||||||||||
| DOI: | 10.1145/3313276.3316369 | |||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||
| Publisher Statement: | © Owner/Author | ACM 2019. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, http://dx.doi.org/10.1145/3313276.3316369. | |||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||
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| Conference Paper Type: | Paper | |||||||||||||||||||||
| Title of Event: | STOC 2019 | |||||||||||||||||||||
| Type of Event: | Conference | |||||||||||||||||||||
| Location of Event: | Phoenix, AZ, USA | |||||||||||||||||||||
| Date(s) of Event: | 23-26 Jun 2019 |
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