Büchi Good-for-Games Automata Are Efficiently Recognizable
Résumé
Good-for-Games (GFG) automata offer a compromise between deterministic and nondetermin-istic automata. They can resolve nondeterministic choices in a step-by-step fashion, without needing any information about the remaining suffix of the word. These automata can be used to solve games with ω-regular conditions, and in particular were introduced as a tool to solve Church's synthesis problem. We focus here on the problem of recognizing Büchi GFG automata, that we call Büchi GFGness problem: given a nondeterministic Büchi automaton, is it GFG? We show that this problem can be decided in P, and more precisely in O(n^4 m^2 |Σ|^2) , where n is the number of states, m the number of transitions and |Σ| is the size of the alphabet. We conjecture that a very similar algorithm solves the problem in polynomial time for any fixed parity acceptance condition.
Domaines
Théorie et langage formel [cs.FL]Origine | Fichiers éditeurs autorisés sur une archive ouverte |
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