A Class of Rational Trace Relations Closed Under Composition

Author Dietrich Kuske

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Dietrich Kuske
  • Technische Universität Ilmenau, Germany


I want to thank the anonymous reviewers whose knowledgeable comments led to a substantial improvement of this paper. This applies in particular to one deep review that pointed out the central role of the composition and its commutation with the natural homomorphism which resulted in clearer and more conceptional proofs.

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Dietrich Kuske. A Class of Rational Trace Relations Closed Under Composition. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Rational relations on words form a well-studied and often applied notion. While the definition in trace monoids is immediate, they have not been studied in this more general context. A possible reason is that they do not share the main useful properties of rational relations on words. To overcome this unfortunate limitation, this paper proposes a restricted class of rational relations, investigates its properties, and applies the findings to systems equipped with a pushdown that does not hold a word but a trace.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • rational relations
  • Mazurkiewicz traces
  • preservation of rationality and recognizability


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