Tiling and local rank properties of the Morse sequence
Theoretical Computer Science
On some generalizations of the Thue--Morse morphism
Theoretical Computer Science
Automatic Sequences: Theory, Applications, Generalizations
Automatic Sequences: Theory, Applications, Generalizations
Fixed Point and Aperiodic Tilings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
DLT'07 Proceedings of the 11th international conference on Developments in language theory
On the frequency of letters in morphic sequences
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Fixed-point tile sets and their applications
Journal of Computer and System Sciences
Hi-index | 0.00 |
We introduce the notion of aperiodicity measure for infinite symbolic sequences. Informally speaking, the aperiodicity measure of a sequence is the maximum number (between 0 and 1) such that this sequence differs 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 fixed 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.