Infinite Separation between General and Chromatic Memory

08/04/2022

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by   Alexander Kozachinskiy, et al.

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In this note, we answer a question from [Alexander Kozachinskiy. State Complexity of Chromatic Memory in Infinite-Duration Games, arXiv:2201.09297]. Namely, we construct a winning condition W over a finite set of colors such that, first, every finite arena has a strategy with 2 states of general memory which is optimal with respect to W, and second, there exists no k such that every finite arena has a strategy with k states of chromatic memory which is optimal with respect to W.