Profile Trees for Büchi Word Automata, with Application to Determinization

Seth Fogarty
(Trinity University)
Orna Kupferman
(Hebrew University of Jerusalem)
Moshe Y. Vardi
(Rice University)
Thomas Wilke
(Christian-Albrechts-Universität zu Kiel)

The determinization of Buchi 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 Buchi 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.

In Gabriele Puppis and Tiziano Villa: Proceedings Fourth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2013), Borca di Cadore, Dolomites, Italy, 29-31th August 2013, Electronic Proceedings in Theoretical Computer Science 119, pp. 107–121.
Published: 16th July 2013.

ArXived at: https://dx.doi.org/10.4204/EPTCS.119.11 bibtex PDF
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