The Geometry of Reachability in Continuous Vector Addition Systems with States

Autor:	Almagor, Shaull, Ghosh, Arka, Leys, Tim, Perez, Guillermo A.
Rok vydání:	2022
Předmět:	Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	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 of fixed dimension. 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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.00785 Zobrazit plný text záznamu View this record from Arxiv