License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2023.18
URN: urn:nbn:de:0030-drops-190120
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/19012/
Bose, Sougata ;
Purser, David ;
Totzke, Patrick
History-Deterministic Vector Addition Systems
Abstract
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.
BibTeX - Entry
@InProceedings{bose_et_al:LIPIcs.CONCUR.2023.18,
author = {Bose, Sougata and Purser, David and Totzke, Patrick},
title = {{History-Deterministic Vector Addition Systems}},
booktitle = {34th International Conference on Concurrency Theory (CONCUR 2023)},
pages = {18:1--18:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-299-0},
ISSN = {1868-8969},
year = {2023},
volume = {279},
editor = {P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/19012},
URN = {urn:nbn:de:0030-drops-190120},
doi = {10.4230/LIPIcs.CONCUR.2023.18},
annote = {Keywords: Vector Addition Systems, History-determinism, Good-for Games}
}
Keywords: |
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Vector Addition Systems, History-determinism, Good-for Games |
Collection: |
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34th International Conference on Concurrency Theory (CONCUR 2023) |
Issue Date: |
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2023 |
Date of publication: |
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07.09.2023 |