Periodicity and local complexity
نویسندگان
چکیده
We consider the complexity of bi-in,nite words in one and two dimensions. A result of Morse and Hedlund in one dimension states that if the complexity, p (n), of a word satis,es p (n)6 n for some n, then the word is periodic. The corresponding question in two dimensions (whether p (m; n)6mn implies that is periodic) is known as the Nivat conjecture. In this paper, we strengthen the one-dimensional result of Morse and Hedlund and prove a weak form of the Nivat conjecture, namely that if for a bi-in,nite two-dimensional word , p (m; n)6mn=16 then is periodic. c © 2004 Published by Elsevier B.V.
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 319 شماره
صفحات -
تاریخ انتشار 2004