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Strategy construction in infinite games with strett and rabin chain winning conditions.pdf

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Strategy construction in infinite games with strett and rabin chain winning conditions

Strategy construction inin nite games with Streett andRabin chain winning conditionsNils BuhrkeHelmut LescowJens VogeABSTRACT We consider nite-state games as a model of nonterminatingreactive computations. A natural type of speci cation is given by gameswith Streett winning condition (corresponding to automata accepting byconjunctions of fairness conditions). We present an algorithm which solvesthe problem of program synthesis for these speci cations. We proceed intwo steps: First, we give a reduction of Streett automata to automata withthe Rabin chain (or parity) acceptance condition. Secondly, we develop aninductive strategy construction over Rabin chain automata which yields nite automata that realize winning strategies. For the step from Rabinchain games to winning strategies examples are discussed, based on animplementation of the algorithm.1 IntroductionIn recent years, methods of automatic veri cation for nite{state programshave been applied successfully, which have clearly reached the level of prac-tical use. For the existing automata theoretic results on nite{state pro-gram synthesis the situation is quite dierent. Not only explicit formula-tions of algorithms but also experience in nontrivial examples are missing.The present paper oers an algorithm for nite{state program synthesisfrom automaton speci cations; we also discuss some examples based on animplementation.The foundations of nite{state program synthesis were laid in the workof Buchi and Landweber [BL69]. Papers exploiting further the approachinclude Pnueli, Rosner [PR89], Abadi, Lamport, Wolper [ALW89], andNerode, Yakhnis, Yakhnis [NYY92]. Recently, the paradigm of programsynthesis has attracted increasing attention in the context of discrete eventInstitut fur Informatikund PraktischeMathematik, Christian-Albrechts-UniversitatKiel, D-24098 Kiel, email: fnb, hel, jvg@informatik.uni-kiel.de. Supported by DeutscheForschungsgemeinschaft, projects Th 352/3-2 and Th 352/5-1. 2 Nils Buhrke,