Church's Problem and a Tour through Automata Theory

Abstract. Church's Problem, stated fifty years ago, asks for a finitestate machine that realizes the transformation of an infinite sequence into an infinite sequence such that a requirement on (, ), 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).

• Type: Conference
• Year: 2008
• Where: BIRTHDAY
• Authors: Wolfgang Thomas
• Keywords: Applied Computing, Automata Theory Play, BIRTHDAY 2008, Infinite Sequence, Monadic Second-order Logic