Abstract
The local behaviour of reversible one-dimensional cellular automata is analysed. Based on Perron–Frobenius theory, it is proved by means of irreducible components that the connectivity matrices of reversible automata have a single eigenvalue equal to 1. The idempotent behaviour of such matrices is also proved by Faddeev's algorithm. The decomposition of these matrices into triangular factors is used to find the inverse rule for a given reversible automaton.
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