Single-valued finite transduction

  • J. Howard Johnson
Formal Languages And Automata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)


Finite state transduction is a simple and effective tool for the efficient analysis and transformation of large bodies of text. However, transductions may yield more than one output for some inputs, an inconvenience in some applications. In principle, multiple output values can be treated in one of the following ways: (1) Consider any input leading to multiple outputs in error. (2) Select the shortest output and consider the input in error if ties remain. (3) Select the genealogical minimum of the possible outputs (minimum length with lexicographic minimum in case of ties). (4) Select the lexicographic minimum of the possible outputs. In cases (3) or (4) a lexicographic order based on a partially-ordered alphabet could be used, with ties resolved as in cases (1) or (2). The naive approach would compute the complete set of outputs and then apply the selection procedure. However, it is possible to combine the selection with the left-to-right computation of the set of outputs using a straight-forward algorithm specified in terms of a *-semiring defined for the strategy selected. The correctness proofs then follow from simple properties of the particular *-semirings. Use of an accessible configurations construction leads to a direct algorithm for computing a minimum-state minimum-delay subsequential transducer for a subsequential function presented as the behaviour of a finite transducer. This machine can be proven to be canonical.


Total Order Lexicographic Order Finite Automaton Oxford English Dictionary Free Monoid 
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.


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  1. [AHU74]
    Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman. Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, Mass, 1974.Google Scholar
  2. [AS85]
    S. Kamal Abdali and B. David Saunders. Transitive closure and related semiring properties via eliminants. Theoretical Computer Science, 40:257–274, 1985.CrossRefGoogle Scholar
  3. [AU72]
    Alfred V. Aho and Jeffrey D. Ullman. The Theory of Parsing, Translation and Compiling, Vol. I: Parsing. Prentice-Hall, Englewood Cliffs, N.J., 1972.Google Scholar
  4. [BC75]
    R. C. Backhouse and B. A. Carré. Regular algebra applied to path-finding problems. J. Inst. Math. Appl., 15:161–186, 1975.Google Scholar
  5. [Ber79]
    Jean Berstel. Transductions and Context-Free Languages. B. G. Teubner, Stuttgart, Germany, 1979.Google Scholar
  6. [Car79]
    B. A. Carré. Graphs and Networks. Clarendon Press, Oxford, 1979.Google Scholar
  7. [Cho77]
    Christian Choffrut. Une caractérisation des fonctions séquentielles et des fonctions sousséquentielles en tant que relations rationnelles. Theoretical Computer Science, 5:325–338, 1977.Google Scholar
  8. [Eil74]
    Samuel Eilenberg. Automata, Languages, and Machines, vol. A. Academic Press, New York, 1974.Google Scholar
  9. [EM65]
    C. C. Elgot and J. E. Mezei. On relations defined by generalized finite automata. IBM Journal of Research, 9:47–65, 1965.Google Scholar
  10. [KS86]
    Werner Kuich and Arto Salomaa. Semirings, Automata, Languages. Springer-Verlag, Berlin, 1986.Google Scholar
  11. [Leh77]
    D. J. Lehmann. Algebraic structures for transitive closure. Theoretical Computer Science, 4(1):59–76, 1977.Google Scholar
  12. [SS78]
    Arto Salomaa and Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag, New York, 1978.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • J. Howard Johnson
    • 1
  1. 1.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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