A Simple Method for Building Bimachines from Functional Finite-State Transducers

  • Stefan Gerdjikov
  • Stoyan MihovEmail author
  • Klaus U. Schulz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10329)


The standard construction of a bimachine from a functional transducer involves a preparation step for converting the transducer into an unambiguous transducer (A transducer is unambiguous if there exists at most one successful path for each label.). The conversion involves a specialized determinization. We introduce a new construction principle where the transducer is directly translated into a bimachine. For any input word accepted by the transducer the bimachine exactly imitates one successful path of the transducer. For some classes of transducers the new construction can build a bimachine with an exponentially lower number of states compared to the standard construction. We first present a simple and generic variant of the construction. A second specialized version leads to better complexity bounds in terms of the size of the bimachine.


Bimachines Transducers Rational functions 


  1. 1.
    Berstel, J.: Transductions and Context-Free Languages. Springer Fachmedien Wiesbaden GmbH, Wiesbaden (1979)Google Scholar
  2. 2.
    Eilenberg, S.: Automata, Languages and Machines. Academic Press, New York and London (1974)zbMATHGoogle Scholar
  3. 3.
    Filiot, E., Servais, F.: Visibly pushdown transducers with look-ahead. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 251–263. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-27660-6_21 CrossRefGoogle Scholar
  4. 4.
    Kempe, A.: Part-of-speech tagging with two sequential transducers. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 337–339. Springer, Heidelberg (2001). doi: 10.1007/3-540-44674-5_34 CrossRefGoogle Scholar
  5. 5.
    Mohri, M.: On some applications of finite-state automata theory to natural language processing. J. Nat. Lang. Eng. 2, 1–20 (1996)CrossRefGoogle Scholar
  6. 6.
    Mohri, M.: Finite-state transducers in language and speech processing. Comput. Linguist. 23(2), 269–311 (1997)MathSciNetGoogle Scholar
  7. 7.
    Roche, E., Schabes, Y.: Finite-State Language Processing. MIT Press, Cambridge (1997)Google Scholar
  8. 8.
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009)Google Scholar
  9. 9.
    Sakarovitch, J., de Souza, R.: Lexicographic decomposition of k-valued transducers. Theor. Comp. Sys. 47(3), 758–785 (2010).
  10. 10.
    Santean, N.: Bimachines and structurally-reversed automata. J. Automata Lang. Comb. 9(1), 121–146 (2004)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Schützenberger, M.P.: A remark on finite transducers. Inf. Control 4, 185–196 (1961)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Souza, R.: A note on bimachines. In: 1a Escola de Informática Teórica e Métodos Formais, Natal - RN, pp. 83–92, November 2016Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Stefan Gerdjikov
    • 1
    • 2
  • Stoyan Mihov
    • 2
    Email author
  • Klaus U. Schulz
    • 3
  1. 1.Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria
  2. 2.Institute of Information and Communication TechnologiesBulgarian Academy of SciencesSofiaBulgaria
  3. 3.Centrum für Informations-und Sprachverarbeitung (CIS)Ludwig-Maximilians-Universität MünchenMünchenGermany

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