Iterated periodicity over finite aperiodic semigroups

• Author(s): Almeida, Jorge ; Costa, José Carlos Cruz da ; Zeitoun, Marc
• Date: 2013
• Persistent ID: http://hdl.handle.net/1822/15034
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Aperiodic semigroup; Free profinite; Pseudoword; omega-term; McCammond normal form; Rational language; Anti-chain; Semigroupoid
• Document Type: Article
• Language: English

Description

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 omega-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 omega-terms that define factors of the given pseudoword. The relationship between pseudowords with this property and arbitrary pseudowords is also investigated.