Pascal Weil

Irreducibility of certain pseudovarieties 1

Communications in Algebra, 1998

We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finii e semigrou... more We prove that the pseudovarieties of all finite semigroups, and of all aperiodic finii e 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 are proved for the pseudovariety of all finite semigroups all of whose subgroups are in a fixed pseudovariety of

CLOSED SUBGROUPS IN PRO-V TOPOLOGIES AND THE EXTENSION PROBLEM FOR INVERSE AUTOMATA

by Mark Sapir and Pascal Weil

International Journal of Algebra and Computation, 2001

We relate the problem of computing the closure of a nitely generated subgroup of the free group i... more We relate the problem of computing the closure of a nitely generated subgroup of the free group in the pro-V topology, where V is a pseudovariety of nite groups, with an extension problem for inverse automata which can be stated as follows: given partial one-to-one maps on a nite set, can they be extended into permutations generating a group in V? The two problems are equivalent when V is extension-closed. Turning to practical computations, we modify Ribes and Zalesski 's algorithm to compute the pro-p closure of a nitely generated subgroup of the free group in polynomial time, and to e ectively compute its pro-nilpotent closure. Finally, we apply our results to a problem in nite monoid theory, the membership problem in pseudovarieties of inverse monoids which are Mal'cev products of semilattices and a pseudovariety of groups. R esum e Nous etablissons un lien entre le probl eme du calcul de l'adh erence d'un sous-groupe niment engendr e du groupe libre dans la topologie pro-V, o u V est une pseudovari et e de groupes nis, et un probl eme d'extension pour les automates inversifs qui peut être enonc e de la fa con suivante : etant donn ees des transformations partielles injectives d'un ensemble ni, peuvent-elles être etendues en des permutations qui engendrent un groupe dans V ? Les deux probl emes sont equivalents si V est ferm ee par extensions. Nous int eressant ensuite aux calculs pratiques, nous modi ons l'algorithme de Ribes et Zalesski pour calculer l'adh erence pro-p d'un sous-groupe niment engendr e du groupe libre en temps polynomial et pour calculer e ectivement sa clôture pro-nilpotente. En n nous appliquons nos r esultats a un probl eme de th eorie des mono des nis, celui de de l'appartenance dans les pseudovari et es de mono des inversifs qui sont des produits de Mal'cev de demi-treillis et d'une pseudovari et e de groupes.

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Free Profinite ℛ-Trivial Monoids

by Pascal Weil and Jorge Almeida

International Journal of Algebra and Computation, 1997

elements of T H (A) by taking the appropriate restriction of the node-labeling function : we then... more elements of T H (A) by taking the appropriate restriction of the node-labeling function : we then talk of decorated subtrees. If r has nitely many children, say n, then H (t) = H (t 1 )a 1 H (t n )a n : Otherwise, r has in nite arity. Let m be the least integer such that the content of the m-th edge descending from r is equal to c (r). Let e be the idempotent designated by the in nite product ( H (t m )a m H (t n )a n ) n m . Then H (t) = H (t 1 )a 1 H (t m?1 )a m?1 ' e ( (r)): Example 5.2.1 Let t ex3 be the following element of T H (A). (The labels in A H of the nodes are between square brackets. We omit the label when it is equal to 1.) y]

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Relatively free profinite monoids: an introduction and examples

by Pascal Weil and Jorge Almeida

Semigroups, Formal Languages and Groups, JB …, 1995

... Projective limits constitute an essential tool for our purpose: to each pseudovariety V and t... more

Series-parallel posets: Algebra, automata and languages

Lecture Notes in Computer Science, 1998

. In order to model concurrency, we extend automata theoryfrom the usual word languages (sets of ... more . In order to model concurrency, we extend automata theoryfrom the usual word languages (sets of labelled linear orders) to setsof labelled series-parallel posets --- or, equivalently, to sets of terms inan algebra with two product operations: sequential and parallel. We firstconsider languages of posets having bounded width, and characterize themusing depth-nilpotent algebras. Next we introduce series-rational expressions,a natural generalization

On a conjecture concerning dot-depth two languages

Theoretical Computer Science, 1992

... So we have R1xu(0)(1)x=R2, Ri.x"u'(0)(1)x=qi, RaYu(1)(0)Y=Ra, R'sYu'(1)(0... more ... So we have R1xu(0)(1)x=R2, Ri.x"u'(0)(1)x=qi, RaYu(1)(0)Y=Ra, R'sYu'(1)(0)Y"=R4 175 for elements ql, Ri, R2, Ri, Ra, R3, R4 and q4 uniquely determined in Q,,. By Lemma 4.4, this implies ql.x uolx=qz 9sYvloY" =9a, Rix"volx=Ri ... [9] J. Green and D. Rees, On semigroups in ...

On Radical Congruence Systems

Semigroup Forum, 1999

R esum e Nous caract erisons les syst emes radicaux de congruences sur les semigroupes nis, qui s... more

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An extension of the wreath product principle for finite Mazurkiewicz traces

Information Processing Letters, 1998

The wreath product principle on words, due to Straubing, has been used, along with the Krohn-Rhod... more

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Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science-STACS 2008

Special issue: Theoretical Aspects of Computer Science, Theory of Computing Systems, vol 47 (3)

Polynomial closure and unambiguous product

Theory of Computing Systems, 1997

... form uoLluj • - - Lnun, where n > 0, the Page 14. 396 J.-E. Pin and E Weil ui's are w... more

PSPACE-complete problems for subgroups of free groups and inverse finite automata

Theoretical Computer Science, 2000

We investigate the complexity of algorithmic problems on finitely generated subgroups of free gro... more We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and effectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this property of H is pspace-complete. In the process, we show that certain problems about finite automata which are pspace-complete in general remain pspace-complete when restricted to injective and inverse automata (with single accept state), whereas they are known to be in NC for permutation automata (with single accept state).

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Relatively free profinite monoids: an introduction and examples

by Pascal Weil and Jorge Almeida

Nato Asi, 1995

... Projective limits constitute an essential tool for our purpose: to each pseudovariety V and t... more

A note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups

by Mark Sapir and Pascal Weil

Publicacions Matemàtiques, 2003

Let V be a pseudovariety of finite groups such that free groups are residually V, and let ϕ: F (A... more Let V be a pseudovariety of finite groups such that free groups are residually V, and let ϕ: F (A) → F (B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extensionφ of ϕ between the pro-V completions of F (A) and F (B) is also injective. In particular, if V is extension-closed, this is the case if and only if ϕ(F (A)) and its pro-V closure in F (B) have the same rank. We examine a number of situations where the injectivity ofφ can be asserted, or at least decided, and we draw a few corollaries.

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Profinite categories and semidirect products

by Pascal Weil and Jorge Almeida

Journal of Pure and Applied Algebra, 1998

After developing a theory of implicit operations and proving an analogue of Reiterman&amp;amp... more After developing a theory of implicit operations and proving an analogue of Reiterman&amp;amp;amp;amp;amp;amp;#39;s theorem for categories, this paper addresses two complementary questions for semidirect products and two-sided semidirect products of pseudovarieties of semigroups: to determine when a pseudoidentity is valid in it, and to find a basis of pseudoidentities. The first question involves looking into the structure of relatively free

UNIFORMITIES ON FREE SEMIGROUPS

International Journal of Algebra and Computation, 1999

Abstract. It is known that the profinite completions of a free semigroup which are associated wit... more Abstract. It is known that the profinite completions of a free semigroup which are associated with a pseudovariety of semigroups or of ordered semigroups, can be defined by an ´ ecart or a quasi-´ ecart. We characterize those quasi-´ ecarts and those quasi-uniformities which arise in this fashion. We also prove an Eilenberg-like one-to-one correspondence between pseudovarieties of ordered semigroups

AUTOMORPHIC ORBITS IN FREE GROUPS: WORDS VERSUS SUBGROUPS

International Journal of Algebra and Computation, 2010

We show that the following problems are decidable in a rank 2 free group F 2

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CLOSED SUBGROUPS IN PRO-V TOPOLOGIES AND THE EXTENSION PROBLEM FOR INVERSE AUTOMATA

International Journal of Algebra and Computation, 2001

We relate the problem of computing the closure of a nitely generated subgroup of the free group i... more We relate the problem of computing the closure of a nitely generated subgroup of the free group in the pro-V topology, where V is a pseudovariety of nite groups, with an extension problem for inverse automata which can be stated as follows: given partial one-to-one maps on a nite set, can they be extended into permutations generating a group in V? The two problems are equivalent when V is extension-closed. Turning to practical computations, we modify Ribes and Zalesski 's algorithm to compute the pro-p closure of a nitely generated subgroup of the free group in polynomial time, and to e ectively compute its pro-nilpotent closure. Finally, we apply our results to a problem in nite monoid theory, the membership problem in pseudovarieties of inverse monoids which are Mal'cev products of semilattices and a pseudovariety of groups.

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25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)

Citeseer, 2010

... Joint work of: Datta, Samir; Kulkarni, Raghav; Roy, Sambuddha Full Paper: http://drops.dagstu... more

Abstracts Collection--25th International Symposium on Theoretical Aspects of Computer Science}

… Aspects of Computer Science (STACS 2008 …, 2008

... Joint work of: Datta, Samir; Kulkarni, Raghav; Roy, Sambuddha Full Paper: http://drops.dagstu... more

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