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Positive Data Languages

Authors Florian Frank , Stefan Milius , Henning Urbat

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


The authors wish to thank Bartek Klin for pointing out the example in Remark 2.10.

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Florian Frank, Stefan Milius, and Henning Urbat. Positive Data Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 48:1-48:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


Positive data languages are languages over an infinite alphabet closed under possibly non-injective renamings of data values. Informally, they model properties of data words expressible by assertions about equality, but not inequality, of data values occurring in the word. We investigate the class of positive data languages recognizable by nondeterministic orbit-finite nominal automata, an abstract form of register automata introduced by Bojańczyk, Klin, and Lasota. As our main contribution we provide a number of equivalent characterizations of that class in terms of positive register automata, monadic second-order logic with positive equality tests, and finitely presentable nondeterministic automata in the categories of nominal renaming sets and of presheaves over finite sets.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Data Languages
  • Register Automata
  • MSO
  • Nominal Sets
  • Presheaves


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