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Regular Separability of Parikh Automata

Authors Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, Charles Paperman

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Lorenzo Clemente
Wojciech Czerwinski
Slawomir Lasota
Charles Paperman

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Lorenzo Clemente, Wojciech Czerwinski, Slawomir Lasota, and Charles Paperman. Regular Separability of Parikh Automata. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 117:1-117:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ICALP.2017.117

Abstract

We investigate a subclass of languages recognized by vector addition systems, namely languages of nondeterministic Parikh automata. While the regularity problem (is the language of a given automaton regular?) is undecidable for this model, we surprisingly show decidability of the regular separability problem: given two Parikh automata, is there a regular language that contains one of them and is disjoint from the other? We supplement this result by proving undecidability of the same problem already for languages of visibly one counter automata.
Keywords
  • Regular separability problem
  • Parikh automata
  • integer vector addition systems
  • visible one counter automata
  • decidability
  • undecidability

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