Aperiodicity Measure for Infinite Sequences
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چکیده
We introduce the notion of aperiodicity measure for in nite symbolic sequences. Informally speaking, the aperiodicity measure of a sequence is the maximum number (between 0 and 1) such that this sequence di ers from each of its non-identical shifts in at least fraction of symbols being this number. We give lower and upper bounds on the aperiodicity measure of a sequence over a xed alphabet. We compute the aperiodicity measure for the Thue{Morse sequence and its natural generalization the Prouhet sequences, and also prove the aperiodicity measure of the Sturmian sequences to be 0. Finally, we construct an automatic sequence with the aperiodicity measure arbitrarily close to 1.
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تاریخ انتشار 2009