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).
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Thomas, W. (2008). Church’s Problem and a Tour through Automata Theory. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds) Pillars of Computer Science. Lecture Notes in Computer Science, vol 4800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78127-1_35
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