Both Ways Rational Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)


We consider binary relations on words which can be recognized by finite two-tape devices in two different ways: the traditional way where the two tapes are scanned in the same direction and a new one where they are scanned in different directions. The devices of the former type define the family of rational relations, while those of the latter define an a priori really different family. We characterize the partial functions that are in the intersection of the two families. We state a conjecture for the intersection for general, nonfunctional, relations.


Rational relations Finite automata Two-way transducers Two-tape automata Word relations 


  1. 1.
    Berstel, J.: Transductions and Context-Free Languages. B. G. Teubner, Stuttgart (1979)CrossRefMATHGoogle Scholar
  2. 2.
    Choffrut, C., Guillon, B.: An algebraic characterization of unary two-way transducers. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014, Part I. LNCS, vol. 8634, pp. 196–207. Springer, Heidelberg (2014)Google Scholar
  3. 3.
    Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, New York (1974)MATHGoogle Scholar
  4. 4.
    Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. 10, 47–68 (1965)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Engelfriet, J., Hoogeboom, H.: MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Log. 2(2), 216–254 (2001)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Fischer, P.C., Rosenberg, A.L.: Multitape one-way nonwriting automata. J. Comput. Syst. Sci. 2(1), 88–101 (1968)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Guillon, B.: Sweeping weakens two-way transducers even with a unary output alphabet. In: Proceedings of Seventh Workshop on NCMA 2015, Porto, Portugal, August 31 – September 1, 2015, pp. 91–108 (2015)Google Scholar
  8. 8.
    Rabin, M., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 125–144 (1959)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, New York (2009)CrossRefMATHGoogle Scholar
  10. 10.
    Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two way finite automata. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, 1–3 May 1978, San Diego, California, USA, pp. 275–286 (1978)Google Scholar
  11. 11.
    Sipser, M.: Lower bounds on the size of sweeping automata. In: Proceedings of the 11th Annual ACM Symposium on Theory of Computing, April 30 – May 2, 1979, Atlanta, Georgia, USA, pp. 360–364 (1979)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.IRIF, CNRS and Université Paris 7 Denis DiderotParisFrance

Personalised recommendations