### On automatic infinite permutations

Anna Frid, Luca Zamboni (2012)

RAIRO - Theoretical Informatics and Applications

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An infinite permutation is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate...