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Solving Sequential Conditions by Finite-State Strategies

  • J. Richard Buchi
  • Lawrence H. Landweber

Abstract

Our main purpose is to present an algorithm which decides whether or not a condition 𝕮(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This solves a problem stated in [4] and contains, as a very special case, the answer to Case 4 left open in [6]. In an equally appealing form the result can be restated in the terminology of [7], [10], [15]: Every ω-game definable in sequential calculus is determined. Moreover the player who has a winning strategy, in fact, has a winning finite-state strategy, that is one which can effectively be played in a strong sense. The main proof, that of the central Theorem 1, will be presented at the end. We begin with a discussion of its consequences.

Keywords

Sequential Condition Finite Automaton Winning Strategy Sequential Calculus Recursive Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • J. Richard Buchi
    • 1
    • 2
  • Lawrence H. Landweber
    • 1
    • 2
  1. 1.Purdue UniversityLafayetteUSA
  2. 2.University of WisconsinMadisonUSA

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