Skip to main content
SpringerLink
Log in

Decomposing a k-valued transducer into k unambiguous ones

  • Conference paper
  • First Online:
LATIN '92 (LATIN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 583))

Included in the following conference series:

Abstract

We investigate the inner structure of finite-valued finite transducers. Our transducer models are the normalized finite transducer (NFT) and the non-deterministic generalized sequential machine (NGSM), which is a real-time NFT. We show: A k-valued NGSM M can be effectively decomposed into k unambiguous NGSMs M1,..., M k such that the transduction realized by M is the union of the transductions realized by M1..., M k . Each M i is of double exponential size and can be constructed in deterministic double exponential time. By reduction, this result can be extended to NFTs. As a consequence, the k-valued and the k-ambiguous NGSMs (NFTs) have the same generative power.

A part of the research for this paper was done while the author was supported by a Postdoctoral Fellowship of the Japan Society for the Promotion of Science.

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.

References

  1. A. Aho, J. Hopcroft and J. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.

    Google Scholar 

  2. J. Berstel, Transductions and Context-free Languages, Teubner, Stuttgart, 1979.

    Google Scholar 

  3. K. Culik II, New techniques for proving the decidability of equivalence problems, Theor. Comput. Sci. 71(1990) 29–45.

    Google Scholar 

  4. S. Eilenberg, Automata, Languages, and Machines, Volume A, Academic Press, New York, NY, 1974.

    Google Scholar 

  5. E. Gurari and O. Ibarra, A note on finite-valued and finitely ambiguous transducers, Math. Syst. Theory 16(1983) 61–66.

    Google Scholar 

  6. J. Hopcroft and J. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979.

    Google Scholar 

  7. J. Karhumäki, The equivalence of mappings on languages, Proc. 4th IMYCS, in: Lect. Notes Comput. Sci., No. 281, Springer-Verlag, Berlin, Heidelberg, 1987, pp. 26–38.

    Google Scholar 

  8. J. Karhumäki, On recent trends in formal language theory, Proc. 14th ICALP, in: Lect. Notes Comput. Sci., No. 267, Springer-Verlag, Berlin, Heidelberg, 1987, pp. 136–162.

    Google Scholar 

  9. L.P. Lisovik, Personal communication, 1991.

    Google Scholar 

  10. R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977.

    Google Scholar 

  11. M.P. Schützenberger, Sur les relations rationnelles entre monoïdes libres, Theor. Comput. Sci. 3(1976) 243–259.

    Google Scholar 

  12. H. Seidl, Equivalence of finite-valued bottom-up finite state tree transducers is decidable, Proc. CAAP 1990, in: Lect. Notes Comput. Sci., No. 431, Springer-Verlag, Berlin, Heidelberg, 1990, pp. 269–284.

    Google Scholar 

  13. R. Stearns and H. Hunt III, On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata, SIAM J. Comput. 14(1985) 598–611.

    Google Scholar 

  14. A. Weber, On the valuedness of finite transducers, Acta Inform. 27(1990) 749–780.

    Google Scholar 

  15. A. Weber, Decomposing finite-valued transducers and deciding their equivalence, SIAM J. Comput., to appear (see also Proc. MFCS 1988, in: Lect. Notes Comput. Sci., No. 324, Springer-Verlag, Berlin, Heidelberg, 1988, pp. 552–562).

    Google Scholar 

  16. A. Weber, On the lengths of values in a finite transducer, Preprint, Goethe-Universität, Frankfurt am Main, 1991 (see also Proc. MFCS 1989, in: Lect. Notes Comput. Sci., No. 379, Springer-Verlag, Berlin, Heidelberg, 1989, pp. 523–533).

    Google Scholar 

  17. A. Weber, A valuedness hierarchy for distance functions, Preprint in preparation, 1991.

    Google Scholar 

  18. A. Weber and R. Klemm, Economy of description for single-valued transducers, Preprint, Goethe-Universität, Frankfurt am Main, 1991.

    Google Scholar 

  19. A. Weber and H. Seidl, On the degree of ambiguity of finite automata, Theor. Comput. Sci. 88(1991) 325–349.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Informatik, J.W. Goethe-Universität, Postfach 111 932, W-6000, Frankfurt am Main 11, Germany

    Andreas Weber

Authors
  1. Andreas Weber
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Imre Simon

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Weber, A. (1992). Decomposing a k-valued transducer into k unambiguous ones. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023852

Download citation

  • DOI: https://doi.org/10.1007/BFb0023852

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55284-0

  • Online ISBN: 978-3-540-47012-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation