Church's problem and a tour through automata theory

  • Authors:
  • Wolfgang Thomas

  • Affiliations:
  • RWTH Aachen, Lehrstuhl Informatik 7, Aachen, Germany

  • Venue:
  • Pillars of computer science
  • Year:
  • 2008

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Abstract

Church's Problem, stated fifty years ago, asks for a finite-state machine that realizes the transformation of an infinite sequence α into an infinite sequence β such that a requirement on (α, β), expressed in monadic second-order logic, is satisfied. We explain how three fundamental techniques of automata theory play together in a solution of Church's Problem: Determinization (starting from the subset construction), appearance records (for stratifying acceptance conditions), and reachability analysis (for the solution of games).