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Irreducibility of Certain Pseudovarieties
"... We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finite semigroups are irreducible for join, for semidirect product and for Mal'cev product. In particular, these pseudovarieties do not admit maximal proper subpseudovarieties. More generally, analogous results ..."
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Cited by 11 (1 self)
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We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finite semigroups are irreducible for join, for semidirect product and for Mal'cev product. In particular, these pseudovarieties do not admit maximal proper subpseudovarieties. More generally, analogous results
A Reiterman theorem for pseudovarieties of finite firstorder structures
, 1996
"... We extend Reiterman's theorem to firstorder structures: a class of finite firstorder structures is a pseudovariety if and only if it is defined by a set of identities in a certain relatively free profinite structure (pseudoidentities) . ..."
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Cited by 20 (13 self)
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We extend Reiterman's theorem to firstorder structures: a class of finite firstorder structures is a pseudovariety if and only if it is defined by a set of identities in a certain relatively free profinite structure (pseudoidentities) .
Syntactic and Global Semigroup Theory, a Synthesis Approach
 in: Algorithmic Problems in Groups and Semigroups
, 2000
"... This paper is the culmination of a series of work integrating syntactic and global semigroup theoretical approaches for the purpose of calculating semidirect products of pseudovarieties of semigroups. We introduce various abstract and algorithmic properties that a pseudovariety of semigroups mig ..."
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Cited by 13 (8 self)
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might possibly satisfy. The main theorem states that given a finite collection of pseudovarieties, each satisfying certain properties of the sort alluded to above, any iterated semidirect product of these pseudovarieties is decidable. In particular, the pseudovariety G of finite groups satisfies
References
, 2009
"... Relatively free profinite semigroups, whose elements are sometimes called pseudowords, have been recognized to play a crucial role in the theory of finite semigroups, namely in the Eilenberg/Schützenberger framework of pseudovarieties, which in turn is the suitable cadre for many applications in com ..."
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in computer science. Yet, only for somewhat small pseudovarieties can one find in the literature structural descriptions of such profinite semigroups. For suitably large pseudovarieties, we construct a natural representation of pseudowords by certain labeled linear orders. In the case of the pseudovariety
Free profinite Rtrivial monoids
"... This article is concerned with the structure of semigroups of implicit operations on R, the pseudovariety of all Rtrivial semigroups. We give two complementary descriptions for these semigroups: first by means of labeled ordinals, and second by means of labeled infinite trees of finite depth. In th ..."
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Cited by 14 (12 self)
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of the corresponding variety of recognizable languages and to the computation of certain joins of pseudovarieties.
The geometry of profinite graphs with applications to free groups and finite monoids
 TRANS AMER. MATH. SOC
, 2003
"... We initiate the study of the class of profinite graphs Γ defined by the following geometric property: for any two vertices v and w of Γ, there is a (unique) smallest connected profinite subgraph of Γ containing them; such graphs are called treelike. Profinite trees in the sense of Gildenhuys and ..."
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Cited by 5 (1 self)
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a certain small cancellation condition. We define a pseudovariety of groups H to be arboreous if all finitely generated free proH groups are dendral (with respect to a free generating set). Our motivation for studying such pseudovarieties of groups is to answer several open questions in the theory
and
"... Abstract. We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pseudovarieties of finite groups and finite aperiodic semigroups. ..."
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Abstract. We consider certain abundant semigroups in which the idempotents form a subsemigroup, and which we call bountiful semigroups. We find a simple criterion for a finite bountiful semigroup to be a member of the join of the pseudovarieties of finite groups and finite aperiodic semigroups.
A CLASSIFICATION OF RATIONAL LANGUAGES BY
"... Abstract. We prove here an Eilenberg type theorem: the socalled conjunctive varieties of rational languages correspond to the pseudovarieties of finite semilatticeordered monoids. Taking complements of members of a conjunctive variety of languages we get a socalled disjunctive variety. We present ..."
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present here a nontrivial example of such a variety together with an equational characterization of the corresponding pseudovariety. Syntactic characterizations of certain significant classes of rational languages were obtained by Schützenberger, Simon, BrzozowskiSimon and McNaughton. It was Eilenberg
Canonical forms for free κsemigroups
, 2013
"... The implicit signature κ consists of the multiplication and the (ω − 1)power. We describe a procedure to transform each κterm over a finite alphabet A into a certain canonical form and show that different canonical forms have different interpretations over some finite semigroup. The procedure of ..."
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Cited by 2 (1 self)
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The implicit signature κ consists of the multiplication and the (ω − 1)power. We describe a procedure to transform each κterm over a finite alphabet A into a certain canonical form and show that different canonical forms have different interpretations over some finite semigroup. The procedure
Finite state automata: A geometric approach
 Trans. Amer. Math. Soc
"... Abstract. Recently, finite state automata, via the advent of hyperbolic and automatic groups, have become a powerful tool in geometric group theory. This paper develops a geometric approach to automata theory, analogous to various techniques used in combinatorial group theory, to solve various probl ..."
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Cited by 22 (13 self)
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problems on the overlap between group theory and monoid theory. For instance, we give a geometric algorithm for computing the closure of a rational language in the profinite topology of a free group. We introduce some geometric notions for automata and show that certain important classes of monoids can
Results 1  10
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