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On the dual post correspondence problem
journal contributionposted on 2015-05-14, 15:05 authored by Joel DayJoel Day, Daniel Reidenbach, Johannes C. Schneider
The Dual Post Correspondence Problem asks whether, for a given word α, there exists a pair of distinct morphisms σ,τ, one of which needs to be non-periodic, such that σ(α) = τ(α) is satisfied. This problem is important for the research on equality sets, which are a vital concept in the theory of computation, as it helps to identify words that are in trivial equality sets only. Little is known about the Dual PCP for words α over larger than binary alphabets, especially for so-called ratio-primitive examples. In the present paper, we address this question in a way that simplifies the usual method, which means that we can reduce the intricacy of the word equations involved in dealing with the Dual PCP. Our approach yields large sets of words for which there exists a solution to the Dual PCP as well as examples of words over arbitrary alphabets for which such a solution does not exist.
This work was supported by the London Mathematical Society, grant SC7-1112-02.
- Computer Science
Published inInternational Journal of Foundations of Computer Science
Pages1033 - 1048
CitationDAY, J.D., REIDENBACH, D. and SCHNEIDER, J.C., 2014. On the dual post correspondence problem. International Journal of Foundations of Computer Science, 25 (8), pp. 1033 - 1048.
Publisher© World Scientific Publishing Co. Pte Ltd
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis article was published in the International Journal of Foundations of Computer Science [© World Scientific Publishing Co. Pte Ltd] and the definitive version is available at: http://dx.doi.org/10.1142/S012905411440022X