For a terminating rewrite system R, and a ground term t 1, two players alternate in doing R-reductions t 1 →R t 2 →R t 3 → R... That is, player 1 choses the redex in t 1, t 3,..., and player 2 choses the redex in t 2, t 4,... The player who cannot move (because t n is a normal form), loses.
In this note, we propose some challenging problems related to certain rewrite games. In particular, we re-formulate an open problem from combinatorial game theory (do all finite octal games have an ultimately periodic Sprague-Grundy sequence?) as a question about rationality of some tree languages.
We propose to attack this question by methods from set constraint systems, and show some cases where this works directly.
Finally we present rewrite games from to combinatory logic, and their relation to algebraic tree languages.
KeywordsNormal Form Period Length Winning Strategy Ground Term Tree Language
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