Advertisement

Two-Way Transducers with a Two-Way Output Tape

  • Olivier Carton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)

Abstract

In this paper, we consider two-way transducers with a two-way output tape. To each cell of the input tape corresponds a cell of the output tape where the transducer can write a finite word. At each transition, the transducer reads one cell of the input tape and either leave unchanged the corresponding cell of the output tape or write a new word into it, overwriting the previous content. We show that each relation realized by such a two-way transducer is rational. It can be realized by a one-way transducer. We also show that any rational function can be realized by a deterministic two-way transducer.

Keywords

Rational Function Expressive Power Empty Word Input Word Input Tape 
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. 1.
    Alur, R., Deshmukh, J.V.: Nondeterministic Streaming String Transducers. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 1–20. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. 2.
    Berstel, J.: Transductions and Context-Free Languages. B.G. Teubner (1979)Google Scholar
  3. 3.
    Choffrut, C.: Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theor. Comput. Sci. 5, 325–337 (1977)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ehrich, R.W., Yau, S.S.: Two-way sequential transductions and stack automata. Information and Control 18(5), 404–446 (1971)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. of Res. and Dev. 9, 47–68 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Engelfriet, J., Hoogeboom, H.J.: MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Log. 2(2), 216–254 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gurari, E.M.: The equivalence problem for deterministic two-way sequential transducers is decidable. SIAM J. Comput. 11(3), 448–452 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Lothaire, M.: Algebraic Combinatorics on Words, ch. 7, pp. 230–268. Cambridge University Press (2002)Google Scholar
  9. 9.
    Schützenberger, M.-P.: Sur les relations rationnelles entre monoïdes libres. Theor. Comput. Sci. 4, 47–57 (1976)CrossRefGoogle Scholar
  10. 10.
    Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM Journal of Research and Development 3, 198–200 (1959)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Olivier Carton
    • 1
  1. 1.LIAFAUniversité Paris Diderot & CNRSFrance

Personalised recommendations