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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: 2013
Publisher: © Springer-Verlag Berlin Heidelberg
Citation: DAY, J.D., REIDENBACH, D. and SCHNEIDER, J.C., 2013. Periodicity forcing words. IN: Karhumäki, J., Lepistö, A.; Zamboni, L. (eds.). Combinatorics on Words: 9th International Conference, WORDS 2013, Turku, Finland, September 16-20, 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): 8079, pp.107-118.
Series/Report no.: Lecture Notes in Computer Science (LCNS);8079
Abstract: The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies 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/prefix/suffix. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already.
Version: Accepted for publication
DOI: 10.1007/978-3-642-40579-2-13
URI: https://dspace.lboro.ac.uk/2134/14011
Publisher Link: http://dx.doi.org/10.1007/978-3-642-40579-2-13
ISBN: 9783642405785
ISSN: 0302-9743
Appears in Collections:Published Articles (Computer Science)

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