Communication Dans Un Congrès Année : 1985

Monoids of upper triangular boolean matrices

Résumé

We study the variety W generated by monoids of upper-triangular boolean matrices. First, we present W as a natural extension of the variety J of finite J-trivial monoids and we give a description of the family of recognizable languages whose syntactic monoids are in W. Then we show that W can be described in terms of the generalized Schützenberger product of finite monoids. We also show that W is generated by the power monoids of members of J. Finally we consider the membership problem for W and the connection with the dot-depth hierarchy in language theory. Although the majority of our results are purely "semigroup-theoretic" we use recognizable languages constantly in the proofs.

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hal-00870684 , version 1 (07-10-2013)

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  • HAL Id : hal-00870684 , version 1

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Jean-Eric Pin, Howard Straubing. Monoids of upper triangular boolean matrices. Semigroups. Structure and Universal AIgebraic Problems, 1981, Szeged, Hungary. pp.259-272. ⟨hal-00870684⟩

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