Unitary monoid with two generators: An algorithmic point of view | SpringerLink
Skip to main content
Springer Nature Link
Log in

Unitary monoid with two generators: An algorithmic point of view

  • Conference paper
  • First Online:
CAAP '90 (CAAP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 431))

Included in the following conference series:

Abstract

We consider the following problem:

Instance: a finite alphabet A, a biprefix code X={x,y} whose elements are primitive, weA*.

Question: find every maximal factors of w which are prefixes of a word of X*.

We present an algorithm which solves the problem in time linear of the length of w, after a preprocessing phase applied to the set X.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aho A and M. Corasick. Efficient String Matching: An Aid to Bibliographic Search, Comm. ACM 18:6 (June 1975), 333–340.

    Article  Google Scholar 

  2. Barbin E. and M. Lerest. Sur la combinatoire des codes à deux mots, Theoret. Comput. Sci., 41 (1985) 61–80.

    Article  Google Scholar 

  3. Berstel J., Perrin D., Perrot J.F. and A. Restivo. Sur le théorème du défaut, Journal of Algebra, Vol 60, No1, September 1979.

    Google Scholar 

  4. Crochemore M. Longest common factor of two words, in TAPSOFT' 87, Springer Lecture Notes in Comput. Sci., 249 (1987) 26–36.

    Google Scholar 

  5. Duval J.P. Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci. 9 (1979) 17–26.

    Article  Google Scholar 

  6. Garey M.and D. Johnson. Computers and intractability. A guide to the Theory of NP-Completeness, W. H. Freeman and Company, 1978.

    Google Scholar 

  7. Hirschberg D and L. Larmore. New Applications of Failure Functions, Journ. of Ass. for Comput. Mach., Vol 34, No3, (July 1987), 616–625.

    Google Scholar 

  8. Hopcroft J. and J. Ullman. Introduction to automata theory, languages and computation, Addison-Wesley publishing company, 1979.

    Google Scholar 

  9. Knuth D., Morris J. and V. Pratt. Fast pattern matching in strings. SIAM J. Comput. 6 (1977) 323–350.

    Article  Google Scholar 

  10. Lentin A. Equations dans le monoïde libre. Pais: Gautier Villars, 1972.

    Google Scholar 

  11. Lerest E. and M.Lerest. Sur les relations entre un nombre fini de mots. Thèse Université de Rouen (France) 1979.

    Google Scholar 

  12. Lentin A. and M.P. Shützenberger. A combinatorial problem in the theory of free monoids, Proc. University of North California (1967) 128–144.

    Google Scholar 

  13. Néraud J. Elementariness of a finite set of words is co-NP-complete, to appear in RAIRO.

    Google Scholar 

  14. Néraud J. On the deficit of a finite set of words, to appear in Semigroup Forum.

    Google Scholar 

  15. Schützenberger M.P. A property of finitely generated submonoids, in: G. Pollak, ed., Algebraic Theory of Semigroups (North-Holland, Amsterdam, 1979) 545–576.

    Google Scholar 

  16. Tarhio J and E. Ukkonen. A greedy approximation algorithm for constructing shortest common superstrings, Theoret. Comput. Sci., 57 (1988) 131–145.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Paris-VII, LITP, 2 place Jussieu, F-75251, Paris Cedex 05

    M. Crochemore

  2. Université de Rouen, LIR, Place Emile Blondel, F-76134, Mont-Saint-Aignan

    J. Neraud

Authors
  1. M. Crochemore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Neraud
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

A. Arnold

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Crochemore, M., Neraud, J. (1990). Unitary monoid with two generators: An algorithmic point of view. In: Arnold, A. (eds) CAAP '90. CAAP 1990. Lecture Notes in Computer Science, vol 431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52590-4_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-52590-4_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52590-5

  • Online ISBN: 978-3-540-47042-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation