An Algorithm for Analyzing the Transitive Behavior of Reversible One-Dimensional Cellular Automata with Both Welch Indices Different

An algorithm is presented for analyzing the transitive behavior of reversible one-dimensional cellular automata, where reversibility refers to injective cellular automata which have a bijective behavior for spatially periodic configurations. In particular we study reversible automata where the ancestors of finite sequences differ at both ends (technically, with both Welch indices different from 1). The algorithm uses the combinatorial properties of reversible automata and their characterization by block permutations. A matrix presentation of the dynamical behavior and examples are presented.

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