2026-08-18T14:22:01Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19012 2024-03-06T11:03:16Z ddc:004 open_access

History-Deterministic Vector Addition Systems Bose, Sougata Purser, David Totzke, Patrick Vector Addition Systems History-determinism Good-for Games We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word. Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without ε-labelled transitions. Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. Checking language inclusion between history-deterministic 2-VASS is also undecidable. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sougata Bose and David Purser and Patrick Totzke 2023 Is Part Of LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2023.18 urn:nbn:de:0030-drops-190120 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.18 eng https://creativecommons.org/licenses/by/4.0/legalcode