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Reachability and Bounded Emptiness Problems of Constraint Automata with Prefix, Suffix and Infix

Authors Jakub Michaliszyn , Jan Otop , Piotr Wieczorek

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Jakub Michaliszyn
  • University of Wrocław, Poland
Jan Otop
  • University of Wrocław, Poland
Piotr Wieczorek
  • University of Wrocław, Poland

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Jakub Michaliszyn, Jan Otop, and Piotr Wieczorek. Reachability and Bounded Emptiness Problems of Constraint Automata with Prefix, Suffix and Infix. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 3:1-3:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We study constraint automata, which are finite-state automata over infinite alphabets consisting of tuples of words. A constraint automaton can compare the words of the consecutive tuples using Boolean combinations of the relations prefix, suffix, infix and equality. First, we show that the reachability problem of such automata is PSpace-complete. Second, we study automata over infinite sequences with Büchi conditions. We show that the problem: given a constraint automaton, is there a bound B and a sequence of tuples of words of length bounded by B, which is accepted by the automaton, is also PSpace-complete. These results contribute towards solving the long-standing open problem of the decidability of the emptiness problem for constraint automata, in which the words can have arbitrary lengths.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • constraint automata
  • emptiness problem


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