Abstract
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. 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Culik II., K.: A purely homomorphic characterization of recursively enumerable sets. Journal of the ACM 26, 345–350 (1979)
Culik II, K., Karhumäki, J.: On the equality sets for homomorphisms on free monoids with two generators. Theoretical Informatics and Applications (RAIRO) 14, 349–369 (1980)
Czeizler, E., Holub, Š., Karhumäki, J., Laine, M.: Intricacies of simple word equations: An example. International Journal of Foundations of Computer Science 18, 1167–1175 (2007)
Engelfriet, J., Rozenberg, G.: Equality languages and fixed point languages. Information and Control 43, 20–49 (1979)
Freydenberger, D.D., Nevisi, H., Reidenbach, D.: Weakly unambiguous morphisms. Theoretical Computer Science 448, 21–40 (2012)
Freydenberger, D.D., Reidenbach, D., Schneider, J.C.: Unambiguous morphic images of strings. International Journal of Foundations of Computer Science 17, 601–628 (2006)
Hadravová, J., Holub, Š.: Large simple binary equality words. International Journal of Foundations of Computer Science 23, 1385–1403 (2012)
Karhumäki, J., Petre, E.: On some special equations on words. Technical Report 583, Turku Centre for Computer Science, TUCS (2003), http://tucs.fi:8080/publications/insight.php?id=tKaPe03a
Lothaire, M.: Combinatorics on Words. Addison-Wesley, Reading (1983)
Mateescu, A., Salomaa, A., Salomaa, K., Yu, S.: P, NP, and the Post Correspondence Problem. Information and Computation 121, 135–142 (1995)
Post, E.L.: A variant of a recursively unsolvable problem. Bulletin of the American Mathematical Society 52, 264–268 (1946)
Reidenbach, D., Schneider, J.C.: Morphically primitive words. Theoretical Computer Science 410, 2148–2161 (2009)
Salomaa, A.: Equality sets for homomorphisms of free monoids. Acta Cybernetica 4, 127–139 (1978)
Schneider, J.C.: Unambiguous erasing morphisms in free monoids. Theoretical Informatics and Applications (RAIRO) 44, 193–208 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Day, J.D., Reidenbach, D., Schneider, J.C. (2013). On the Dual Post Correspondence Problem. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-38771-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38770-8
Online ISBN: 978-3-642-38771-5
eBook Packages: Computer ScienceComputer Science (R0)