Profile trees for Büchi word automata, with application to determinization

Seth Fogarty*, Orna Kupferman, Moshe Y. Vardi, Thomas Wilke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The determinization of Büchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra, Piterman, Schewe, and others. Despite the proliferation of solutions, they are all essentially ad-hoc constructions, with little theory behind them other than proofs of correctness. Since Safra, all optimal constructions employ trees as states of the deterministic automaton, and transitions between states are defined operationally over these trees. The operational nature of these constructions complicates understanding, implementing, and reasoning about them, and should be contrasted with complementation, where a solid theory in terms of automata run dags underlies modern constructions. In 2010, we described a profile-based approach to Büchi complementation, where a profile is simply the history of visits to accepting states. We developed a structural theory of profiles and used it to describe a complementation construction that is deterministic in the limit. Here we extend the theory of profiles to prove that every run dag contains a profile tree with at most a finite number of infinite branches. We then show that this property provides a theoretical grounding for a new determinization construction where macrostates are doubly preordered sets of states. In contrast to extant determinization constructions, transitions in the new construction are described declaratively rather than operationally.

Original languageAmerican English
Pages (from-to)136-151
Number of pages16
JournalInformation and Computation
Volume245
DOIs
StatePublished - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.

Keywords

  • Automata theory
  • Büchi determinization
  • Büchi profiles
  • Omega-automata
  • ω-automata

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