On Factorization Forests of Finite Height

Jérémie Chalopin (1) , H. Leung (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 CS - Department of Computer Science of NMSU

Simon [3] has proved that every morphism from a free semigroup to a finite semigroup S admits a Ramseyan factorization forest of height at most 9jSj. In this paper, we prove the same result of Simon with an improved bound of 7jSj. We provide a simple algorithm for constructing a factorization forest. In addition, we show that the algorithm cannot be improved significantly. We give examples of semigroup morphism such that any Ramseyan factorization forest for the morphism would require a height not less than

Domaines: Autre [cs.OH]

Jérémie Chalopin, H. Leung. On Factorization Forests of Finite Height. Theoretical Computer Science, 2004, 310, pp.489--499. ⟨hal-00308120⟩