History-Deterministic Parikh Automata

Authors Enzo Erlich, Shibashis Guha , Ismaël Jecker , Karoliina Lehtinen , Martin Zimmermann

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Author Details

Enzo Erlich
  • ENS Rennes, France
Shibashis Guha
  • Tata Institute of Fundamental Research, Mumbai, India
Ismaël Jecker
  • University of Warsaw, Poland
Karoliina Lehtinen
  • CNRS, Aix-Marseille University, LIS, France
Martin Zimmermann
  • Aalborg University, Denmark

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Enzo Erlich, Shibashis Guha, Ismaël Jecker, Karoliina Lehtinen, and Martin Zimmermann. History-Deterministic Parikh Automata. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure properties of deterministic automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Parikh automata
  • History-determinism
  • Reversal-bounded Counter Machines


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