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Lexicographic Decomposition of k-Valued Transducers

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Abstract

We give a new, and hopefully more easily understandable, structural proof of the decomposition of a k-valued transducer into k unambiguous functional ones, a result established by A. Weber in 1996. Our construction is based on a lexicographic ordering of computations of automata and on two coverings that can be build by means of this ordering. The complexity of the construction, measured as the number of states of the transducers involved in the decomposition, improves the original one by one exponential.

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Authors and Affiliations

  1. LTCI, ENST/CNRS, Paris, France

    Jacques Sakarovitch

  2. DEINFO, Universidade Federal Rural de Pernambuco, Campus Universitário da UFRPE, Dois Irmãos, CEP 52171-900, Recife, PE, Brazil

    Rodrigo de Souza

Authors
  1. Jacques Sakarovitch
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  2. Rodrigo de Souza
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Correspondence to Rodrigo de Souza.

Additional information

A preliminary version of this paper has been presented at the STACS 2008 conference under the title On the decomposition of k -valued rational relations [20].

A financial support of CAPES Foundation (Brazilian government) for doctoral studies is gratefully acknowledged by R. de Souza.

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Sakarovitch, J., de Souza, R. Lexicographic Decomposition of k-Valued Transducers. Theory Comput Syst 47, 758–785 (2010). https://doi.org/10.1007/s00224-009-9206-6

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  • DOI: https://doi.org/10.1007/s00224-009-9206-6

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