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Abstract: The Besicovitch pseudodistance measures the relative size of the set ofpoints where two functions take different values; the quotient space modulo theinduced equivalence relation is endowed with a natural metric. We study thebehavior of cellular automata in the new topology and show that, under suitableadditional hypotheses, they retain certain properties possessed in the usualproduct topology; in particular, that injectivity still implies surjectivity.



Author: Silvio Capobianco

Source: https://arxiv.org/







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