Iterated periodicity over finite aperiodic semigroups

Jorge Almeida (1) , José-Carlos Costa (2) , Marc Zeitoun (3)

1 UNIVERSIDADE DO PORTO - Departamento de Matemática Pura, Faculdade de Ciências
2 CMAT - Centro de Matemática [Minho]
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique

This paper provides a characterization of pseudowords over the pseudovariety of all finite aperiodic semigroups that can be described from the free generators using only the operations of multiplication and ω-power. A necessary and sufficient condition for this property to hold turns out to be given by the conjunction of two rather simple finiteness conditions: the nonexistence of infinite anti-chains of factors and the rationality of the language of McCammond normal forms of ω-terms that define factors of the given pseudoword. The relationship between pseudowords with this property and arbitrary pseudowords is also investigated.

Mots clés: Aperiodic semigroup. Free profinite semigroup. Pseudoword. ω-term. McCammond normal form. Rational language. Anti-chain. Semigroupoid.; Aperiodic semigroup. Free profinite semigroup. Pseudoword. ω-term. McCammond normal form. Rational language. Anti-chain. Semigroupoid

Domaines: Théorie et langage formel [cs.FL]; Anneaux et algèbres [math.RA]

Jorge Almeida, José-Carlos Costa, Marc Zeitoun. Iterated periodicity over finite aperiodic semigroups. European Journal of Combinatorics, 2014, 37, pp.115-149. ⟨hal-00948999⟩