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Article Dans Une Revue Journal of Computer and System Sciences Année : 2012

Schützenberger and Eilenberg theorems for words on linear orderings

Résumé

This paper contains extensions to words on countable scattered linear orderings of two well-known results of characterization of languages of finite words. We first extend a theorem of Schützenberger establishing that the star-free sets of finite words are exactly the languages recognized by finite aperiodic semigroups. This gives an algebraic characterization of star-free sets of words over countable scattered linear orderings. Contrarily to the case of finite words, first-order definable languages are strictly included into the star-free languages when countable scattered linear orderings are considered. Second, we extend the variety theorem of Eilenberg for finite words: there is a one-to-one correspondence between varieties of languages of words on countable scattered linear orderings and pseudo-varieties of algebras. The star-free sets are an example of such a variety of languages.

Dates et versions

hal-00790098 , version 1 (19-02-2013)

Identifiants

Citer

Nicolas Bedon, Chloé Rispal. Schützenberger and Eilenberg theorems for words on linear orderings. Journal of Computer and System Sciences, 2012, 78 (2), pp.517-536. ⟨10.1016/j.jcss.2011.06.003⟩. ⟨hal-00790098⟩
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