Counting and hardness-of-finding fixed points in cellular automata on random graphs
Cédric Koller,
Freya Behrens,
Lenka Zdeborová
Abstract:We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on its state and the total number of its neighbors in each possible state. Examples of this setting include classical problems such as independent sets or assortative/dissasortative partitions. We analyse the existence and number of fixed points in the large system limit using th… Show more
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