Abstract
We consider a restricted variant of the prefix-suffix duplication operation, called bounded prefix-suffix duplication. It consists in the iterative duplication of a prefix or suffix, whose length is bounded by a constant, of a given word. We give a sufficient condition for the closure under bounded prefix-suffix duplication of a class of languages. Consequently, the class of regular languages is closed under bounded prefix-suffix duplication; furthermore, we propose an algorithm deciding whether a regular language is a finite k-prefix-suffix duplication language. An efficient algorithm solving the membership problem for the k-prefix-suffix duplication of a language is also presented. Finally, we define the k-prefix-suffix duplication distance between two words, extend it to languages and show how it can be computed for regular languages.
Florin Manea’s work is supported by the DFG grant 596676. Victor Mitrana’s work is partially supported by the Alexander von Humboldt Foundation.
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.
References
Bovet, D.P., Varricchio, S.: On the regularity of languages on a binary alphabet generated by copying systems. Inform. Proc. Letters 44(3), 119–123 (1992)
Crochemore, M.: An optimal algorithm for computing the repetitions in a word. Inf. Process. Lett. 12(5), 244–250 (1981)
Dassow, J., Mitrana, V., Păun, G.: On the regularity of duplication closure. Bull. European Assoc. Theor. Comput. Sci. 68, 133–136 (1999)
Ehrenfeucht, A., Rozenberg, G.: On the separating power of EOL systems. RAIRO Inform. Theor. 17(1), 13–22 (1983)
Frazier, M., David Page Jr., C.: Prefix grammars: an alternative characterization of the regular languages. Inf. Process. Lett. 2, 67–71 (1994)
Garcia Lopez, J., Manea, F., Mitrana, V.: Prefix-suffix duplication. J. Comput. Syst. Sci. (in press) doi:10.1016/j.jcss.2014.02.011
Ginsburg, S.: Algebraic and automata-theoretic properties of formal languages. North-Holland Pub. Co. (1975)
Gusfield, D.: Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge University Press, New York (1997)
Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM 53(6), 918–936 (2006)
Leupold, P.: Reducing repetitions. In: Prague Stringology Conf., pp. 225–236 (2009)
Papadimitriou, C.: Computational Complexity. Addison-Wesley (1994)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. I–III. Springer, Berlin (1997)
Searls, D.B.: The computational linguistics of biological sequences. In: Artificial Intelligence and Molecular Biology, pp. 47–120. MIT Press, Cambridge (1993)
Wang, M.-W.: On the irregularity of the duplication closure. Bull. European Assoc. Theor. Comput. Sci. 70, 162–163 (2000)
Knuth, D.: The Art of Computer Programming, 3rd edn. Fundamental Algorithms, vol. 1, pp. 238–243. Addison-Wesley (1997), Section 2.2.1: Stacks, Queues, and Deques, ISBN 0-201-89683-4
Knuth, D., Morris, J.H., Pratt, V.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Dumitran, M., Gil, J., Manea, F., Mitrana, V. (2014). Bounded Prefix-Suffix Duplication. In: Holzer, M., Kutrib, M. (eds) Implementation and Application of Automata. CIAA 2014. Lecture Notes in Computer Science, vol 8587. Springer, Cham. https://doi.org/10.1007/978-3-319-08846-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-08846-4_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08845-7
Online ISBN: 978-3-319-08846-4
eBook Packages: Computer ScienceComputer Science (R0)