Multi-sequential Word Relations

  • Ismaël JeckerEmail author
  • Emmanuel Filiot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


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.


Rational Relation Sequential Function Input Word Free Monoid Strongly Connect Component 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Université Libre de BruxellesBrusselBelgium

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