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Journal Articles Communications in Algebra Year : 2002

The wreath product principle for ordered semigroups

Abstract

Straubing's wreath product principle provides a description of the languages recognized by the wreath product of two monoids. A similar principle for ordered semigroups is given in this paper. Applications to language theory extend standard results of the theory of varieties to positive varieties. They include a characterization of positive locally testable languages and syntactic descriptions of the operations L ? La and L ? LaA*. Next we turn to concatenation hierarchies. It was shown by Straubing that the n-th level Bn of the dot-depth hierarchy is the variety Vn * LI, where LI is the variety of locally trivial semigroups and Vn is the n-th level of the Straubing-Thérien hierarchy. We prove that a similar result holds for the half levels. It follows in particular that a level or a half level of the dot-depth hierarchy is decidable if and only if the corresponding level of the Straubing-Thérien hierarchy is decidable.
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Dates and versions

hal-00112618 , version 1 (09-11-2006)

Identifiers

  • HAL Id : hal-00112618 , version 1

Cite

Jean-Eric Pin, Pascal Weil. The wreath product principle for ordered semigroups. Communications in Algebra, 2002, 30, pp.5677-5713. ⟨hal-00112618⟩
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