Manuel Delgado

Approximation to the smallest regular expression for a given regular language

A regular expression that represents the language accepted by a given finite automaton can be obtained using the the state elimination algorithm. The order of vertex removal affects the size of the resulting expression. We use here an heuristic to compute an approximation to the order of vertex removal that leads to the smallest regular expression obtainable this way.

TAMENESS OF THE PSEUDOVARIETY OF ABELIAN GROUPS

In this paper we prove that the pseudovariety of Abelian groups is hyperdecidable and moreover that it is completely tame. This is a consequence of the fact that a system of group equations on a free Abelian group with certain rational constraints is solvable if and only if it is solvable in every finite quotient.

numericalsgps, a GAP package for numerical semigroups

The package numericalsgps performs computations with and for numerical and affine semigroups. This manuscript is a survey of what the package does, and at the same time intends to gather the trending topics on numerical semigroups.

On the Weight Hierarchy of Codes Coming From Semigroups With Two Generators

The weight hierarchy of one-point algebraic geometry codes can be estimated by means of the generalized order bounds, which are described in terms of a certain Weierstrass semigroup. The asymptotical behavior of such bounds for r ≥ 2 differs from that of the classical Feng-Rao distance (r=1) by the so-called Feng-Rao numbers. This paper is addressed to compute the Feng-Rao numbers for numerical semigroups of embedding dimension two (with two generators), obtaining a closed simple formula for the general case by using numerical semigroup techniques. These involve the computation of the Apéry set with respect to an integer of the semigroups under consideration. The formula obtained is applied to lower bounding the generalized Hamming weights, improving the bound given by Kirfel and Pellikaan in terms of the classical Feng-Rao distance. We also compare our bound with a modification of the Griesmer bound, improving this one in many cases.

ON THE HYPERDECIDABILITY OF PSEUDOVARIETIES OF GROUPS

Clarifying the relation between Ashs (algebraic-combinatorial) proof and Ribes and Zalesskis (topological) proof of the Rhodes Type II conjecture is an intriguing and interesting question which arose when both proofs appeared in the beginning of the 1990s. Attempting to contribute to this clarification, we observe that two sets, each playing a crucial role in one of the proofs, are in fact equal. The equality of these sets allows us to give an alternative proof of part of the main theorem of Ashs paper where the hyperdecidability of the pseudovariety of all finite groups is established.

COMBINATORIAL GROUP THEORY, INVERSE MONOIDS, AUTOMATA, AND GLOBAL SEMIGROUP THEORY

This paper explores various connections between combinatorial group theory, semigroup theory, and formal language theory. Let G = be a group presentation and ℬA, R its standard 2-complex. Suppose X is a 2-complex with a morphism to ℬA, R which restricts to an immersion on the 1-skeleton. Then we associate an inverse monoid to X which algebraically encodes topological properties of the morphism. Applications are given to separability properties of groups. We also associate an inverse monoid M(A, R) to the presentation with the property that pointed subgraphs of covers of ℬA, R are classified by closed inverse submonoids of M(A, R). In particular, we obtain an inverse monoid theoretic condition for a subgroup to be quasiconvex allowing semigroup theoretic variants on the usual proofs that the intersection of such subgroups is quasiconvex and that such subgroups are finitely generated. Generalizations are given to non-geodesic combings. We also obtain a formal language theoretic equivalence to quasiconvexity which holds even for groups which are not hyperbolic. Finally, we illustrate some applications of separability properties of relatively free groups to finite semigroup theory. In particular, we can deduce the decidability of various semidirect and Mal/cev products of pseudovarieties of monoids with equational pseudovarieties of nilpotent groups and with the pseudovariety of metabelian groups.

Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid

In this paper we do not make a clear distinction between what is introduction and preliminaries. In fact, we have decided to put it all in a single section which is divided into 3 subsections. The first, concerning kernels of finite monoids and related properties, should mainly serve as a general motivation for the study that we will do later with some particular classes of monoids. In the second subsection are introduced those classes of monoids.

Commutative images of rational languages and the abelian kernel of a monoid

Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm which allows the direct computation of the closure in the profinite topology of the commutative image. As an application, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice.

On the generalized Feng-Rao numbers of numerical semigroups generated by intervals

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the

Solvable monoids with commuting idempotents

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