Advertisement

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

  • K. CulikII
  • J. Karhumäki
Conference paper
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ACK]
    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.CrossRefzbMATHGoogle Scholar
  2. [AL]
    Albert, M.H. and Lawrence, J., A proof of Ehrenfeucht's Conjecture, Theoret. Comput. Sci. 41 (1985) 121–123.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [B]
    Berstel, J., Transductions and Context-Free Languages (Teubner, Stuttgrard, 1979).CrossRefzbMATHGoogle Scholar
  4. [CC]
    Culik II, K., and Choffrut, C., Properties of finite and pushdown transducers, SIAM, J. Comput. 12 (1983) 300–315.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [CK1]
    Culik II, K., and Karhumäki, J., Systems of equations over a free monoid and Ehrenfeucht's Conjecture, Discrete Mathematics 43 (1983) 139–153.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [CK2]
    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. [CS]
    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. [ERS]
    Engelfriet, J., Rozenberg, G., and Stutzki, G., Tree transducers, L systems and two-way machines, J. Comput. Systems Sci. 20 (1980) 150–202.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [Gr]
    Griffiths, T., The unsolvability of the equivalence problem for ε-free nondeterministic generalized machines, J. Assoc. Comput. Mach. 15 (1968) 409–413.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [Gu]
    Guba, V.S., personal communication (1985).Google Scholar
  11. [H]
    Harrison, M.A., Introduction to Formal Language Theory (Addison-Wesley, Reading MA, 1982).zbMATHGoogle Scholar
  12. [HK]
    Harju, T., and Karhumäki, J., On the defect theorem and simplifiability, semigroup Forum 33 (1986) 199–217.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [HKK]
    Horváth, S., Karhumäki, J., and Kleijn, H.C.M., Decidability and characterization results concerning palindromicity, EIK, to appear.Google Scholar
  14. [K]
    Karhumäki, J., The Ehrenfeucht Conjecture: A compactness claim for finitely generated free monoids, Theoret. Comput. Sci. 29 (1984) 285–308.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Mak]
    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).MathSciNetzbMATHGoogle Scholar
  16. [Mar]
    Markov, Al. A., On finitely generated subsemigroups of a free semigroup, Semigroup Forum 3 (1971) 251–258.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [NRSS]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [S]
    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. [RS]
    Rozenberg, G., and Salomaa, A., The Mathematical Theory of L Systems (Academic Press, New York, 1980).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • K. CulikII
  • J. Karhumäki

There are no affiliations available

Personalised recommendations