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Multi-sequential Word Relations

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A particular kind of rational relations is the sequential functions. Sequential functions are the functions that can be realised by input-deterministic transducers. Some rational functions are not sequential. However, based on a property on transducers called the twinning property, it is decidable in PTime whether a rational function given by an NFT is sequential. In this paper, we investigate the generalisation of this result to multi-sequential relations, i.e. relations that are equal to a finite union of sequential functions. We show that given an NFT, it is decidable in PTime whether the relation it defines is multi-sequential, based on a property called the fork property. If the fork property is not satisfied, we give a procedure that effectively constructs a finite set of input-deterministic transducers whose union defines the relation. This procedure generalises to arbitrary NFT the determinisation procedure of functional NFT.

I. Jecker—Author supported by the ERC inVEST (279499) project.

E. Filiot—F.R.S.-FNRS research associate (chercheur qualifié).

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Authors and Affiliations

  1. Université Libre de Bruxelles, Brussel, Belgium

    Ismaël Jecker & Emmanuel Filiot

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  1. Ismaël Jecker
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  2. Emmanuel Filiot
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Correspondence to Ismaël Jecker .

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Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Jecker, I., Filiot, E. (2015). Multi-sequential Word Relations. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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