Decidable Containment Problems of Rational Word Relations

  • Wojciech FraczakEmail author
  • Stéphane Hassen
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 110)


We study a particular case of the inclusion problem for rational relations over words. The problem consists in checking whether a submonoid, M, is included in a rational relation, R. We show that if M is rational and commutative then the problem MR is decidable. In the second part of the paper we study the inclusion problem, M↓R, where M is a commutative submonoid and ↓R is the prefix-closure of a rational word relation R. We describe an algorithm which solves the problem in a polynomial time, assuming that the number of tapes (arity of the word relation) is constant.


Formal language Multi-tape automata Rational relation Inclusion 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Dépt d’informatique et d’ingénierieUniversité du Québec en OutaouaisGatineauCanada

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