Recognizing pro-R closures of regular languages

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 semigroups generated by the pseudovariety R of all finite R-trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by R-languages

Canonical forms for free k-semigroups

The implicit signature kappa consists of the multiplication and the (omega-1)-power. We describe a procedure to transform each kappa-term 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 construction of the canonical forms, which is inspired in McCammond's normal form algorithm for omega-termsninterpreted over the pseudovariety A of all finite aperiodic semigroups, consists in applying elementary changes determined by an elementary set Sigma of pseudoidentities. As an application, we deduce that the variety of kappa-semigroups generated by the pseudovariety S of all finite semigroups is defined by the set Sigma and that the free kappa-semigroup generated by the alphabet A in that variety has decidable word problem. Furthermore, we show that each omega-term has a unique omega-term in canonical form with the same value over A. In particular, the canonical forms provide new, simpler, representatives for omega-terms interpreted over that pseudovariety.European Regional Development Fund, through the programme COMPETEFundação para a Ciência e a Tecnologia (FCT), under the project PEst-C/MAT/UI0013/2011

Some variations on the notion of locally testable language

The aim of this paper is to complete the characterization of the languages that are Boolean combinations (of a subset) of languages of the form wA*, A*w or L(w; r; t; n), where A is an alphabet, w is a finite word, r; t are non-negative integers, n is a positive integer and L(w; r; t; n) denotes the set of all words u in A+ such that the number of occurrences of the factor w in u is congruent to r threshold t mod n. For each class C of languages such that A+C is a Boolean algebra generated by some of the following types of languages: wA*, A*w, A*wA*= L(w; 1; 1; 1) or L(w; r; t; 1), and such that C does not constitute a variety of languages, we compute the smallest variety of languages containing C and the largest variety of languages contained in C

Free profinite semigroups over some classes of semigroups locally in DG

This paper is concerned with the structure of semigroups of implicit operations on various subpseudovarieties V of DReG intersection with LDG, where DReG and DG are the pseudovarieties of all semigroups S in which each regular D-class is, respectively, a rectangular group and a group, and where LDG is the pseudovariety of semigroups locally in DG. As an application, we give a characterization of the variety of languages recognized by semigroups in V and derive some join decompositions of pseudovarieties.INVOTAN, grant 4/A/94/P

Sesuvium syntaxa nomenclatura correction of Cabo Verde islands

info:eu-repo/semantics/publishedVersio

Some pseudovariety joins involving locally trivial semigroups

This paper is concerned with the computation of pseudovariety joins involving the pseudovariety LI of locally trivial semigroups. We compute, in particular, the join of LI with any subpseudovariety of CRmN, the Mal'cev product of the pseudovariety of completely regular semigroups and the pseudovariety of nilpotent semigroups. Similar studies are conducted for the pseudovarieties K, D and N, where K (resp. D) is the pseudovariety of all semigroups S such that eS = e (resp. Se = e ) for each idempotent e of S.INVOTAN, grant 4/A/94/P

Some pseudovariety joins involving locally trivial semigroups and groups

In this paper, we present the computation of some pseudovariety joins of the form LI v H v V where LI is the pseudovariety of locally trivial semigroups and H is any pseudovariety of groups. Similar results are obtained for the pseudovarieties K, of semigroups in which idempotents are left zeros, and its dual D, in the place of LI.FCT through the Centro de Matemática da Universidade do MinhoEuropean Community Fund FEDE