Skip to main content

Systems of equations over a finitely generated free monoid having an effectively findable equivalent finite subsystem

Part of the Lecture Notes in Mathematics book series (LNM,volume 1320)

Abstract

It has been proved recently, cf, [AL], that each system of equations over a finitely generated free monoid having only a finite number of variables has an equivalent finite subsystem. We discuss the problem when such a finite subsystem can be effectively found. We show that this is the case when the system is defined by finite, algebraic or deterministic two-way transducers.

Keywords

  • Binary Relation
  • Regular Language
  • Compactness Property
  • Free Semigroup
  • Free Monoid

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-2403

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, J., Culik II, K. and Karhumäki, J., Test sets for context-free languages and algebraic systems of equations, Inform. Control 52 (1982) 172–186.

    CrossRef  MATH  Google Scholar 

  2. Albert, M.H. and Lawrence, J., A proof of Ehrenfeucht's Conjecture, Theoret. Comput. Sci. 41 (1985) 121–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Berstel, J., Transductions and Context-Free Languages (Teubner, Stuttgrard, 1979).

    CrossRef  MATH  Google Scholar 

  4. Culik II, K., and Choffrut, C., Properties of finite and pushdown transducers, SIAM, J. Comput. 12 (1983) 300–315.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Culik II, K., and Karhumäki, J., Systems of equations over a free monoid and Ehrenfeucht's Conjecture, Discrete Mathematics 43 (1983) 139–153.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Culik II, K., and Karhumäki, J., The decidability of the DTOL sequence equivalence problem and related decision problems, University of Waterloo, Department of Computer Science, Research Report CS-85-05 (1985).

    Google Scholar 

  7. Culik II, K., and Salomaa, A., On the Decidability of Homomorphism Equivalence for Languages, J. Comput. System Sci. 17 (1978) 163–175.

    Google Scholar 

  8. Engelfriet, J., Rozenberg, G., and Stutzki, G., Tree transducers, L systems and two-way machines, J. Comput. Systems Sci. 20 (1980) 150–202.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Griffiths, T., The unsolvability of the equivalence problem for ε-free nondeterministic generalized machines, J. Assoc. Comput. Mach. 15 (1968) 409–413.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Guba, V.S., personal communication (1985).

    Google Scholar 

  11. Harrison, M.A., Introduction to Formal Language Theory (Addison-Wesley, Reading MA, 1982).

    MATH  Google Scholar 

  12. Harju, T., and Karhumäki, J., On the defect theorem and simplifiability, semigroup Forum 33 (1986) 199–217.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Horváth, S., Karhumäki, J., and Kleijn, H.C.M., Decidability and characterization results concerning palindromicity, EIK, to appear.

    Google Scholar 

  14. Karhumäki, J., The Ehrenfeucht Conjecture: A compactness claim for finitely generated free monoids, Theoret. Comput. Sci. 29 (1984) 285–308.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Makanin, G.S., The Problem of solvability of equations in a free semigroup, Mat. Sb. 103 (1977) 147–236 (English transl. in: Math USSR Sb. 32 (1977) 129–198).

    MathSciNet  MATH  Google Scholar 

  16. Markov, Al. A., On finitely generated subsemigroups of a free semigroup, Semigroup Forum 3 (1971) 251–258.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Nielsen, M., Rozenberg, G., Salomaa, A. and Skyum S., Nonterminals, homomorphisms and codings in different variations of OL-systems, I. Deterministic systems, Acta Informatica 4 (1974) 87–106.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Spehner,J.-C., Tout sous-monoide finiment engendré d'un monoide libre admet une présentation de Malcev finie, C.R. Acad. Sc. Paris, 301, Série I, no. 18 (1985).

    Google Scholar 

  19. Rozenberg, G., and Salomaa, A., The Mathematical Theory of L Systems (Academic Press, New York, 1980).

    MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Culik, K., Karhumäki, J. (1988). Systems of equations over a finitely generated free monoid having an effectively findable equivalent finite subsystem. In: Jürgensen, H., Lallement, G., Weinert, H.J. (eds) Semigroups Theory and Applications. Lecture Notes in Mathematics, vol 1320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083421

Download citation

  • DOI: https://doi.org/10.1007/BFb0083421

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19347-0

  • Online ISBN: 978-3-540-39225-5

  • eBook Packages: Springer Book Archive