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Title: Periodicity forcing words
Authors: Day, Joel D.
Reidenbach, Daniel
Schneider, Johannes C.
Keywords: Equality sets
Dual Post Correspondence Problem
Periodicity forcing sets
Periodicity forcing words
Ambiguity of morphisms
Issue Date: 2015
Publisher: © Elsevier
Citation: DAY, J.D., REIDENBACH, D. and SCHNEIDER, J.C., 2015. Periodicity forcing words. Theoretical Computer Science, 601, pp. 2-14.
Abstract: The Dual Post Correspondence Problem asks, for a given word , if there exists a non-periodic morphism g and an arbitrary morphism h such that g( ) = h( ). Thus satis es the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of morphisms. In this paper, a `prime' subset of periodicity forcing words is presented. It is shown that when combined with a particular type of morphism it generates exactly the full set of periodicity forcing words. Furthermore, it is shown that there exist examples of periodicity forcing words which contain any given factor/pre x/su x. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already.
Description: This paper was accepted for publication in the journal Theoretical Computer Science and the definitive published version is available at: http://dx.doi.org/10.1016/j.tcs.2015.08.033
Sponsor: This work was supported by the London Mathematical Society, grant SC7-1112-02.
Version: Accepted for publication
DOI: 10.1016/j.tcs.2015.08.033
URI: https://dspace.lboro.ac.uk/2134/18420
Publisher Link: http://dx.doi.org/10.1016/j.tcs.2015.08.033
ISSN: 0304-3975
Appears in Collections:Published Articles (Computer Science)

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