Decidable Containment Problems of Rational Word Relations
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 M ⊆ R 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.
KeywordsFormal language Multi-tape automata Rational relation Inclusion
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