Separating Regular Languages over Infinite Words with Respect to the Wagner Hierarchy

Author Christopher Hugenroth

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Christopher Hugenroth
  • TU Ilmenau, Germany


I want to thank Christof Löding who supervised my Master thesis on which this paper is based and Dietrich Kuske for clarifying discussions. Further, I want to thank the reviewers of former versions of this paper for their helpful suggestions.

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Christopher Hugenroth. Separating Regular Languages over Infinite Words with Respect to the Wagner Hierarchy. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 46:1-46:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We investigate the separation problem for regular ω-languages with respect to the Wagner hierarchy where the input languages are given as deterministic Muller automata (DMA). We show that a minimal separating DMA can be computed in exponential time and that some languages require separators of exponential size. Further, we show that in this setting it can be decided in polynomial time whether a separator exists on a certain level of the Wagner hierarchy and that emptiness of the intersection of two languages given by DMAs can be decided in polynomial time. Finally, we show that separation can also be decided in polynomial time if the input languages are given as deterministic parity automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • Theory of computation → Regular languages
  • Separation
  • Regular
  • Wagner Hierarchy
  • Muller Automata
  • Parity Automata
  • Product Automata
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