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Suppose that a deterministic finite automata A = (Q, ⌃) is such that all but one letters from the alphabet ⌃ act as permutations of the state set Q and the exceptional letter acts as a transformation with non-uniform kernel. Which properties of the permutation group G generated by the letters acting as permutations ensure that A becomes a synchronizing… (More)

In this note we give an elementary proof of a theorem first proved by J. A. Erdos [3]. This theorem, which is the main result of [3], states that every noninvertible n × n matrix is a finite product of matrices M with the property that M 2 = M. (These are known as idempotent matrices. Noninvertible matrices are also called singular matrices.) An alternative… (More)

In ubiquitous streaming data sources, such as sensor networks, clustering nodes by the data they produce is an important problem that gives insights on the phenomenon being monitored by such networks. However, if these techniques require data to be gathered centrally, communication and storage requirements are often unbounded. The goal of this paper is to… (More)

In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the… (More)

Independence algebras were introduced in the early 1990s by specialists in semigroup theory, as a tool to explain similarities between the transformation monoid on a set and the endomorphism monoid of a vector space. It turned out that these algebras had already been defined and studied in the 1960s, under the name of v *-algebras, by specialists in… (More)

Let S be a finite non-commutative semigroup. The commuting graph of S, denoted G(S), is the graph whose vertices are the non-central elements of S and whose edges are the sets {a, b} of vertices such that a = b and ab = ba. Denote by T (X) the semigroup of full transformations on a finite set X. Let J be any ideal of T (X) such that J is different from the… (More)

Let ⌦ be a set of cardinality n, G a permutation group on ⌦, and f : ⌦ ! ⌦ a map which is not a permutation. We say that G synchronizes f if the semigroup hG, f i contains a constant map. The first author has conjectured that a primitive group synchronizes any map whose kernel is non-uniform. Rystsov proved one instance of this conjecture, namely, degree n… (More)

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices.

— Industrial monitoring of complex processes with hundreds or thousands of variables is a hard task faced in this work through evolving fuzzy systems. The Visbreaker process of the Sines Oil Refinery is the case studied. Firstly dimension reduction is performed by multidimensional scaling, obtaining the process evolution in a three dimensional space. Then… (More)