Typeness for ω-regular automata

Orna Kupferman*, Gila Morgenstern, Aniello Murano

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class γ (that is, γ is weak, Büchi, co-Büchi, Rabin, or Streett), deterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same deterministic structure, nondeterministic γ-typeness asks for the existence of an equivalent γ-automaton on the same structure, and γ-powerset-typeness asks for the existence of an equivalent γ-automaton on the (deterministic) powerset structure -one obtained by applying the subset construction. The notions are helpful in studying the complexity and complication of translations between the various classes of automata. For example, we prove that deterministic Büchi automata are co-Büchi type; it follows that a translation from deterministic Büchi to deterministic co-Büchi automata, when exists, involves no blow up. On the other hand, we prove that nondeterministic Büchi automata are not co-Büchi type; it follows that a translation from a nondeterministic Büchi to nondeterministic co-Büchi automata, when exists, should be more complicated than just redefining the acceptance condition. As a third example, by proving that nondeterministic co-Büchi automata are Büchi-powerset type, we show that a translation of nondeterministic co-Büchi to deterministic Büchi automata, when exists, can be done applying the subset construction. We give a complete picture of typeness for the weak, Büchi, co-Büchi, Rabin, and Streett acceptance conditions, and discuss its usefulness.

Original languageAmerican English
Pages (from-to)869-883
Number of pages15
JournalInternational Journal of Foundations of Computer Science
Volume17
Issue number4
DOIs
StatePublished - 1 Aug 2006

Keywords

  • Acceptance conditions
  • Automata on infinite words

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