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Minimizing GFG Transition-Based Automata (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Bader Abu Radi, Orna Kupferman



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Bader Abu Radi
  • School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel
Orna Kupferman
  • School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel

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Bader Abu Radi and Orna Kupferman. Minimizing GFG Transition-Based Automata (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 100:1-100:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ICALP.2019.100

Abstract

While many applications of automata in formal methods can use nondeterministic automata, some applications, most notably synthesis, need deterministic or good-for-games automata. The latter are nondeterministic automata that can resolve their nondeterministic choices in a way that only depends on the past. The minimization problem for nondeterministic and deterministic Büchi and co-Büchi word automata are PSPACE-complete and NP-complete, respectively. We describe a polynomial minimization algorithm for good-for-games co-Büchi word automata with transition-based acceptance. Thus, a run is accepting if it traverses a set of designated transitions only finitely often. Our algorithm is based on a sequence of transformations we apply to the automaton, on top of which a minimal quotient automaton is defined.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Automata over infinite objects
Keywords
  • Minimization
  • Deterministic co-Büchi Automata

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