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Boolean Combinations of ω-Rational Trace Languages: Emptiness, Rationality, Regularity

Author Dietrich Kuske

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Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Regular languages
Keywords
  • Mazurkiewicz traces
  • rational and regular languages
  • degrees of unsolvability

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Abstract

This paper studies decision problems for Boolean combinations of ω-rational trace languages. The complexities of these decision problems (emptiness, regularity, rationality) are classified depending on properties of the independence alphabets and of the Boolean combinations allowed. For any of the problems, we obtain a trichotomy ranging from decidable over a low level of the arithmetical hierarchy to a low level of the analytical hierarchy.

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Dietrich Kuske. Boolean Combinations of ω-Rational Trace Languages: Emptiness, Rationality, Regularity. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.17

Author Details

Dietrich Kuske
  • Technische Universität Ilmenau, Germany

References

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