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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 Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving:… (More)

- Jorge Almeida
- 1996

Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of nite semi-groups. Some of these problems aaord equivalent formulations involving topological separation properties in free proonite semigroups. Several examples are considered and, as… (More)

- Jorge Almeida
- IJAC
- 1999

This note introduces the notion of a hyperdecidable pseudovariety. This notion appears naturally in trying to prove decidability of the membership problem of semidirect products of pseudovarieties of semigroups. It turns out to be a generalization of a notion introduced by C. J. Ash in connection with his proof of the \type II" theorem. The main results in… (More)

Profinite semigroups may be described shortly as projective limits of finite semigroups. They come about naturally by studying pseudovarieties of finite semigroups which in turn serve as a classifying tool for rational languages. Of particular relevance are relatively free profinite semigroups which for pseudovarieties play the role of free algebras in the… (More)

- Jorge Almeida
- 1999

This work gives a new approach to the construction of implicit operations. By considering “higher-dimensional” spaces of implicit operations and implicit operators between them, the projection of idempotents back to one-dimensional spaces produces implicit operations with interesting properties. Besides providing a wealth of examples of implicit operations… (More)

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus… (More)

- Jorge Almeida, Pascal Weil
- IJAC
- 1994

- Jorge Almeida
- IJAC
- 1996

We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite pro-identity basis for the pseudovariety H of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.

- Jorge Almeida, Mikhail V. Volkov
- IJAC
- 2006

We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated implicit operators, subword complexity and the associated entropy.