77 citations · 154 across the 22 of their papers we have counts for
23 papers
Equidivisibility and profinite coproduct
Jorge Almeida, Alfredo Costa
The aim of this work is to investigate the behavior of equidivisibility under coproduct in the category of pro- semigroups, where is a pseudovariety of fin…
What makes a Stone topological algebra profinite
Jorge Almeida, Herman Goulet-Ouellet, Ondřej Klíma
This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate and simplify proofs for some kno…
Stone pseudovarieties
Jorge Almeida, Ondřej Klíma
Profinite algebras are the residually finite compact algebras; their underlying topological spaces are Stone spaces. We extend the theory of profinite algebras to a more general se…
Locally countable pseudovarieties
Jorge Almeida, Ondrej Klíma
The purpose of this paper is to contribute to the theory of profinite semigroups by considering the special class consisting of those all of whose finitely generated closed subsemi…
Recognizing pro-R closures of regular languages
Jorge Almeida, José Carlos Costa, Marc Zeitoun
Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary sem…
Binary patterns in the Prouhet-Thue-Morse sequence
Jorge Almeida, Ondřej Klíma
We show that, with the exception of the words and , all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that seq…
On the group of a rational maximal bifix code
Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou +1
We give necessary and sufficient conditions for the group of a rational maximal bifix code to be isomorphic with the -group of , when is recurrent and …
Pseudovarieties of ordered completely regular semigroups
Jorge Almeida, Ondřej Klíma
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The questi…
Profinite topologies
Jorge Almeida, Alfredo Costa
Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite sem…
On the insertion of n-powers
J. Almeida, O. Klíma
In algebraic terms, the insertion of -powers in words may be modelled at the language level by considering the pseudovariety of ordered monoids defined by the inequality $1\le x…
Towards a pseudoequational proof theory
Jorge Almeida, Ondřej Klíma
A new scheme for proving pseudoidentities from a given set Σ of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when Σ defines a l…
Nilpotency and strong nilpotency for finite semigroups
J. Almeida, M. Kufleitner, M. H. Shahzamanian
Nilpotent semigroups in the sense of Mal'cev are defined by semigroup identities. Finite nilpotent semigroups constitute a pseudovariety, , which has finite rank. The…
The linear nature of pseudowords
Jorge Almeida, Alfredo Costa, José Carlos Costa +1
Given a pseudoword over suitable pseudovarieties, we associate to it a labeled linear order determined by the factorizations of the pseudoword. We show that, in the case of the pse…
Commutative positive varieties of languages
Jorge Almeida, Zoltán Ésik, Jean-Éric Pin
We study the commutative positive varieties of languages closed under various operations: shuffle, renaming and product over one-letter alphabets.
Reducibility versus definability for pseudovarieties of semigroups
J. Almeida, O. Klíma
It is easy to show that a pseudovariety which is reducible with respect to an implicit signature for the equation can also be defined by -identities. We present severa…
Equidivisible pseudovarieties of semigroups
Jorge Almeida, Alfredo Costa
We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free profinite semigroups are equidivisible. Besides the pseudovarieties of…
The omega-inequality problem for concatenation hierarchies of star-free languages
J. Almeida, O. Klíma, M. Kunc
The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows th…
Complete kappa-reducibility of pseudovarieties of the form DRH
Jorge Almeida, Célia Borlido
We denote by kappa the implicit signature that contains the multiplication and the (omega-1)-power. It is proved that for any completely kappa-reducible pseudovariety of groups H,…
A geometric interpretation of the Schützenberger group of a minimal subshift
J. Almeida, A. Costa
The first author has associated in a natural way a profinite group to each irreducible subshift. The group in question was initially obtained as a maximal subgroup of a free profin…
Factoriality and the Pin-Reutenauer procedure
J. Almeida, J. C. Costa, M. Zeitoun
We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigr…
McCammond's normal forms for free aperiodic semigroups revisited
Jorge Almeida, José Carlos Costa, Marc Zeitoun
This paper revisits the solution of the word problem for -terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCa…
Presentations of Schutzenberger groups of minimal subshifts
Jorge Almeida, Alfredo Costa
In previous work, the first author established a natural bijection between minimal subshifts and maximal regular J-classes of free profinite semigroups. In this paper, the Schützen…
Representation Theory of Finite Semigroups, Semigroup Radicals and Formal Language Theory
Jorge Almeida, Stuart Margolis, Benjamin Steinberg +1
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of…