Atlas Talk: The Reachability Problem for Petri Nets is Not Elementary
|Dates:||3 February 2021|
|Times:||14:00 - 15:00|
|What is it:||Seminar|
|Organiser:||Department of Computer Science|
|Who is it for:||University staff, Adults|
Join us for the next Computer Science Atlas Talk (online)
Join here: https://zoom.us/j/93918368182
Speaker: Ranko Lazic - University of Warwick
Host: Ian Pratt-Hartmann
Title: The Reachability Problem for Petri Nets is Not Elementary
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 con?guration there exists a sequence of valid execution steps that reaches the given ?nal con?guration. 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 veri?cation. 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.
Joint work with Wojciech Czerwinski, Slawomir Lasota, Jerome Leroux and Filip Mazowiecki.
Organisation: University of Warwick
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