Varieties of Data Languages (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Henning Urbat, Stefan Milius

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Henning Urbat
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Stefan Milius
  • Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

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Henning Urbat and Stefan Milius. Varieties of Data Languages (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 130:1-130:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal monoids and pseudovarieties of such monoids. This is the first result of this kind for data languages. Our approach makes use of nominal Stone duality and a recent category theoretic generalization of Birkhoff-type theorems that we instantiate here for the category of nominal sets. In addition, we prove an axiomatic characterization of weak pseudovarieties as those classes of orbit-finite monoids that can be specified by sequences of nominal equations, which provides a nominal version of a classical theorem of Eilenberg and Schützenberger.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Nominal sets
  • Stone duality
  • Algebraic language theory
  • Data languages


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