Families of DFAs as acceptors of ω-regular languages

Dana Angluin, Udi Boker, Dana Fisman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations


Families of dfas (fdfas) provide an alternative formalism for recognizing ω-regular languages. The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages. This correlation is beneficial for learning algorithms, and indeed it was recently shown that ω-regular languages can be learned from membership and equivalence queries, using fdfas as the acceptors. In this paper, we look into the question of how suitable fdfas are for defining ω-regular languages. Specifically, we look into the complexity of performing Boolean operations, such as complementation and intersection, on fdfas, the complexity of solving decision problems, such as emptiness and language containment, and the succinctness of fdfas compared to standard deterministic and nondeterministic ω-automata. We show that fdfas enjoy the benefits of deterministic automata with respect to Boolean operations and decision problems. Namely, they can all be performed in nondeterministic logarithmic space. We provide polynomial translations of deterministic Büchi and co-Büchi automata to fdfas and of fdfas to nondeterministic Büchi automata (nbas). We show that translation of an nba to an fdfa may involve an exponential blowup. Last, we show that fdfas are more succinct than deterministic parity automata (dpas) in the sense that translating a dpa to an fdfa can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case.

Original languageEnglish
Title of host publication41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016
EditorsAnca Muscholl, Piotr Faliszewski, Rolf Niedermeier
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770163
StatePublished - 1 Aug 2016
Externally publishedYes
Event41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016 - Krakow, Poland
Duration: 22 Aug 201626 Aug 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016


  • Finite automata
  • Omega Regular Languages

ASJC Scopus subject areas

  • Software


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