Reachability in Vector Addition Systems is Ackermann-complete

Vector Addition Systems and equivalent Petri nets are a well established models of concurrency. The central algorithmic problem for Vector Addition Systems with a long research history is the reachability problem asking whether there exists a run from one given configuration to another. We settle it...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1229 - 1240
Main Authors: Czerwinski, Wojciech, Orlikowski, Lukasz
Format: Conference Proceeding
Language:English
Published: IEEE 01.02.2022
Subjects:
ackermann completeness
Complexity theory
Computer science
Concurrent computing
History
Petri nets
reachability problem
vector addition systems
ISSN:2575-8454
Online Access:Get full text
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Summary:Vector Addition Systems and equivalent Petri nets are a well established models of concurrency. The central algorithmic problem for Vector Addition Systems with a long research history is the reachability problem asking whether there exists a run from one given configuration to another. We settle its complexity to be Ackermann-complete thus closing the problem open for 45 years. In particular we prove that the problem is \mathcal{F}_{k} -hard for Vector Addition Systems with States in dimension 6k, where \mathcal{F}_{k} is the k -th complexity class from the hierarchy of fast-growing complexity classes.
ISSN:2575-8454
DOI:10.1109/FOCS52979.2021.00120