Chapter

Developments in Language Theory

Volume 5257 of the series Lecture Notes in Computer Science pp 529-542

Complexity of Topological Properties of Regular ω-Languages

  • Victor L. SelivanovAffiliated withSiberian Division of the Russian Academy of Sciences, A.P. Ershov Institute of Informatics Systems
  • , Klaus W. WagnerAffiliated withInstitut für Informatik, Julius-Maximilians-Universität Würzburg

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Abstract

We determine the complexity of topological properties of regular ω-languages (i.e., classes of ω-languages closed under inverse continuous functions). We show that they are typically NL-complete (PSPACE-complete) for the deterministic Muller, Mostowski and Büchi automata (respectively, for the nondeterministic Rabin, Muller, Mostowski and Büchi automata). For the deterministic Rabin and Streett automata and for the nondeterministic Streett automata upper and lower complexity bounds for the topological properties are established.