Skip to main content
SpringerLink
Log in

On the Equivalence of Finite Substitutions and Transducers

  • Chapter
Jewels are Forever

Summary

This paper discusses on several variants of a fascinating problem of deciding whether two finite substitutions are equivalent on a regular language, as well as its relations to the equivalence problems of sequential transducers. Among other things it is proved to be decidable whether for a regular language L and two substitutions ϕ and ψ the latter one being a prefix substitution, the relation Unknown control sequence φ(w) ⊆ ψ (w) holds for all w in L.

This work was initiated when this author visited Turku University under the grant 14047 of the Academy of Finland.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berstel, J., Transductions and Context-Pree Languages, Teubner, Stuttgart, 1979.

    Google Scholar 

  2. Bird, M., The equivalence problem for deterministic two-tape automata, J. Comput. System Sei. 7, 1973, 218–236.

    Article  MathSciNet  MATH  Google Scholar 

  3. Culik II, K. and Karhumäki, J., The equivalence of finite valued transducers (on HDTOL languages) is decidable, Theoret. Comput. Sei. 47, 1986, 71–84.

    Article  MATH  Google Scholar 

  4. Culik II, K. and Fris, I., The decidability of the equivalence problem for D0L-systems, Inform, and Control 33, 1976, 20–33.

    Google Scholar 

  5. Culik II, K. and Salomaa, A., On the decidability of homomorphism equivalence for languages, J. Comput. System. Sei 17, 1978, 163–175.

    Article  MathSciNet  Google Scholar 

  6. Griffiths, T.V., The unsolvability of the equivalence problem for A-free non-deterministic generalized machines, J. Assoc. Comput. Mach. 15, 1968, 409–413.

    MathSciNet  MATH  Google Scholar 

  7. Gurari, E. and Ibarra, O., The complexity of decision problems for finite-turn multicounter machines, J. Comput. System Sei. 22, 1981, 220–229.

    Article  MathSciNet  MATH  Google Scholar 

  8. Haiava, V., Finite substitutions and integer weighted finite automata, Turku Centre for Computer Science, TUCS Report 197, 1998.

    Google Scholar 

  9. Haiava, V. and Harju, T., Undecidability of the equivalence of finite substitutions on regular language, RAIRO Theoret. Informatics and Applications (to appear).

    Google Scholar 

  10. Harju, T. and Karhumäki, J., The equivalence problem of multitape finite automata, Theoret. Comp. Sei. 78, 1991, 345–353.

    Google Scholar 

  11. Harju, T. and Karhumäki, J., Morphisms, in: G. Rozenberg and A. Salomaa (eds), Handbook of Formal Languages, Vol. I, Springer, 1997, 439–510.

    Chapter  Google Scholar 

  12. Hopcroft, J.E. and Ullman J.D., Introduction to Automata Theory, Languages and Computation, Addison-Wesley, 1973.

    Google Scholar 

  13. Ibarra, O., The unsolvability of the equivalence problem for ε-free NGSM’s with unary input (output) alphabet and applications, SIAM J. Comput. 7, 1978, 524–532.

    Article  MathSciNet  MATH  Google Scholar 

  14. Karhumäki, J., Equations on finite sets of words and equivalence problems in automata theory, Theoret. Comput. Sei. 108, 1993, 103–118.

    Article  MATH  Google Scholar 

  15. Karhumäki, J. and Kleijn, H.C.M., On the equivalence of compositions of morphisms and inverse morphisms on regular languages, RAIRO Theor. Informatics 19, 1985, 203–211.

    MATH  Google Scholar 

  16. Lawrence, J., The non-existence of finite test sets for set equivalence of finite substitutions, Bull. EATCS 28, 1986, 34–37.

    MATH  Google Scholar 

  17. Lisovik, L.P., The identity problem of regular events over cartesian product of free and cyclic semigroups, Doklady of Academy of Sciences of Ukraina 6, 1979, 480–413.

    Google Scholar 

  18. Lisovik, L.P., The equivalence problem for finite substitutions on regular language, Doklady of Academy of Sciences of Russia 357, 1997, 299–301.

    MathSciNet  Google Scholar 

  19. Lisovik, L.P., The equivalence problems for transducers with bounded number of states, Kibernetika and Sistemny Analiz 6, 1997, 109–114.

    MathSciNet  Google Scholar 

  20. Perrin, D., Codes conjegués, Inform, and Control 20, 1972, 221–231.

    MathSciNet  Google Scholar 

  21. Senizergues, G., L(A) = L(B) ?, Manuscript, 1998.

    Google Scholar 

  22. Turakainen, P., The undecidability of some equivalence problems concerning ngsm’s and finite substitutions, Theoret. Comput. Sei. 174, 1997, 269–274.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Juhani Karhumäki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonid P. Lisovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Turku Centre for Computer Science, University of Turku, FIN-20014, Turku, Finland

    Juhani Karhumäki

  2. Institutes for Information Processing and Computer Supported Media (IICM), Technical University of Graz, Schiessstattgasse 4a, A-8010, Graz, Austria

    Hermann Maurer

  3. Institute of Mathematics, Romanian Academy of Sciences, PO Box l-764, RO-70700, Bucharest, Romania

    Gheorghe Păun

  4. Department of Computer Science, Leiden University, PO Box 9512, 2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Karhumäki, J., Lisovik, L.P. (1999). On the Equivalence of Finite Substitutions and Transducers. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds) Jewels are Forever. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60207-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-60207-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64304-0

  • Online ISBN: 978-3-642-60207-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation