Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T08:21:11.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Unambiguous erasing morphisms in free monoids

Published online by Cambridge University Press:  07 December 2009

Johannes C. Schneider
Johannes C. Schneider*
Affiliation:
Fachbereich Informatik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany; [email protected]
Get access

Abstract

This paper discusses the fundamental combinatorial question of whether or not, for a given string α, there exists a morphism σ such that σ is unambiguous with respect to α, i.e. there exists no other morphism τ satisfying τ(α) = σ(α). While Freydenberger et al. [Int. J. Found. Comput. Sci. 17 (2006) 601–628] characterise those strings for which there exists an unambiguous nonerasing morphism σ, little is known about the unambiguity of erasing morphisms, i.e. morphisms that map symbols onto the empty string. The present paper demonstrates that, in contrast to the main result by Freydenberger et al., the existence of an unambiguous erasing morphism for a given string can essentially depend on the size of the target alphabet of the morphism. In addition to this, those strings for which there exists an erasing morphism over an infinite target alphabet are characterised, complexity issues are discussed and some sufficient conditions for the (non-)existence of unambiguous erasing morphisms are given.

Keywords

Combinatorics on wordsmorphisms in free monoidsunambiguitycomplexity
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 2 , April 2010 , pp. 193 - 208
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C. Choffrut and J. Karhumäki, Combinatorics of words, edited by G. Rozenberg and A. Salomaa, Handbook of Formal Languages 1, Chap. 6. Springer (1997) 329–438.
Ehrenfeucht, A. and Rozenberg, G., Finding a homomorphism between two words is NP-complete. Inform. Process. Lett. 9 (1979) 86–88. CrossRef
D.D. Freydenberger and D. Reidenbach, The unambiguity of segmented morphisms. In Proc. 11th International Conference on Developments in Language Theory, DLT 2007. Lect. Notes Comput. Sci. (2007) 181–192.
Freydenberger, D.D., Reidenbach, D. and Schneider, J.C., Unambiguous morphic images of strings. Int. J. Found. Comput. Sci. 17 (2006) 601–628. CrossRef
M.R. Garey and D.S. Johnson, Computers and Intractability – A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979).
Head, T., Fixed languages and the adult languages of 0L schemes. Int. J. Comput. Math. 10 (1981) 103–107. CrossRef
Jiang, T., Salomaa, A., Salomaa, K. and Decision, S. Yu problems for patterns. J. Comput. System Sci. 50 (1995) 53–63. CrossRef
A. Mateescu and A. Salomaa, Patterns, edited by G. Rozenberg and A. Salomaa, Handbook of Formal Languages 1, Chap. 4.6. Springer (1997) 230–242.
Reidenbach, D., A non-learnable class of E-pattern languages. Theoret. Comput. Sci. 350 (2006) 91–102. CrossRef
Reidenbach, D., Discontinuities in pattern inference. Theoret. Comput. Sci. 397 (2008) 166–193. CrossRef
D. Reidenbach and J.C. Schneider, Morphically primitive words, in Proc. 6th International Conference on Words, WORDS 2007 (2007) 262–272.
Schneider, J.C., Unambiguous erasing morphisms in free monoids, in Proc. SOFSEM 2009: Theorie and Practice of Computer Science. Lect. Notes Comput. Sci. 5404 (2009) 473–484. CrossRef