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Over Which Monoids is the Transducer Determinization Procedure Applicable?

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Language and Automata Theory and Applications (LATA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

Abstract

The input determinization of a finite-state transducer for constructing an equivalent subsequential transducer is performed by the well-known inductive transducer determinization procedure. This procedure has been shown to complete for rational functions with the bounded variation property. The result has been obtained for functions \(f : \varSigma ^*\rightarrow \mathcal {M}\), where \(\mathcal {M}\) is a free monoid, the monoid of non-negative real numbers with addition or a Cartesian product of those monoids. In this paper we generalize this result and define and prove sufficient conditions for a monoid \(\mathcal {M}\) and a rational function \(f : \varSigma ^*\rightarrow \mathcal {M}\), under which the transducer determinization procedure is applicable and terminates.

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Notes

  1. 1.

    It can be easily shown that \(d_\mathcal {M}\) is a distance.

  2. 2.

    This assumption is not a significant limitation since if it is not the case we can modify the state output function to output the desired word \(\alpha \) for the starting state on the resulting subsequential transducer.

  3. 3.

    That is we ignore the output produced by \(\mathcal {M}_{j}\) for \(j\ne i\).

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Sofia University, 5, James Borchier Blvd., 1164, Sofia, Bulgaria

    Stefan Gerdjikov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 25A, Acad. G. Bonchev Street, 1113, Sofia, Bulgaria

    Stefan Gerdjikov & Stoyan Mihov

Authors
  1. Stefan Gerdjikov
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  2. Stoyan Mihov
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Corresponding author

Correspondence to Stoyan Mihov .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Gerdjikov, S., Mihov, S. (2017). Over Which Monoids is the Transducer Determinization Procedure Applicable?. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_28

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

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