The Geometry of Reachability in Continuous Vector Addition Systems with States

Shaull Almagor, Arka Ghosh, Tim Leys, Guillermo A. Pérez

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the geometry of reachability sets of continuous vector addition systems with states (VASS). In particular we establish that they are “almost” Minkowski sums of convex cones and zonotopes generated by the vectors labelling the transitions of the VASS. We use the latter to prove that short so-called linear path schemes suffice as witnesses of reachability in continuous VASS. Then, we give new polynomial-time algorithms for the reachability problem for linear path schemes. Finally, we also establish that enriching the model with zero tests makes the reachability problem intractable already for linear path schemes of dimension two.

Original languageEnglish
Title of host publication48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023
EditorsJerome Leroux, Sylvain Lombardy, David Peleg
ISBN (Electronic)9783959772921
DOIs
StatePublished - Aug 2023
Event48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023 - Bordeaux, France
Duration: 28 Aug 20231 Sep 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume272

Conference

Conference48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023
Country/TerritoryFrance
CityBordeaux
Period28/08/231/09/23

Keywords

  • Vector addition system with states
  • continuous approximation
  • reachability

All Science Journal Classification (ASJC) codes

  • Software

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