Decidable Containment Problems of Rational Word Relations
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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
- 6.Fraczak W, Hassen S (2011) A decidable instance of the inclusion problem for rational relations. In The International MultiConference of Engineers and Computer Scientists 2011, IMECS 2011, Lecture Notes in Engineering and Computer Science, Hong KongGoogle Scholar
- 9.Habermehl P, Mayr R (2000) A note on SLRE. Technical report, LIAFA - Universit Denis Diderot, 2, place Jussieu, Paris Cedex 05, FranceGoogle Scholar
- 12.Klarlund N (1998) Mona & fido: The logic-automaton connection in practice. In: Selected Papers from the11th International Workshop on Computer Science Logic, CSL ’97, Springer, London, UK, pp 311–326Google Scholar
- 15.Stockmeyer LJ, Meyer AR (1973) Word problems requiring exponential time (Preliminary Report). In: Proceedings of the fifth annual ACM symposium on Theory of computing, STOC ’73, ACM, New York, NY, USA, pages 1–9Google Scholar