A defect theorem for bi-infinite words

Authors:
Juhani Karhumäki;Ján Manuch;Wojciech Plandowski
Affiliations:
Department of Mathematics, Turku Centre for Computer Science, University of Turku, Turku, Finland;Department of Mathematics, Turku Centre for Computer Science, University of Turku, Turku, Finland;Department of Mathematics, Turku Centre for Computer Science, University of Turku, Turku, Finland
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We formulate and prove a defect theorem for bi-infinite words. Let X be a finite set of words over a finite alphabet. If a nonperiodic bi-infinite word w has two X-factorizations, then the combinatorial rank of X is at most card(X)- 1, i.e., there exists a set F such that X ⊆ F+ with card(F) card(X). Moreover, in the case when the combinatorial rank of X equals card(X), the number of periodic bi-infinite words which have two different X-factorizations is finite.