A note on the reversibility of the elementary cellular automaton with rule number 90

The reversibility properties of the elementary cellular automaton with rule number 90 are studied. It is shown that the cellular automaton considered is not reversible when periodic boundary conditions are considered, whereas when null boundary conditions are stated, the reversibility appears when the number of cells of the cellular space is even. The DETGTRI algorithm is used to prove these statements. Moreover, the explicit expressions of inverse cellular automata of reversible ones are computed.

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