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- Yanqing Duan, Roisin Mullins, +5 authors Joao Araujo
- 2003

- João Araújo, Wolfram Bentz, Peter J. Cameron
- Theor. Comput. Sci.
- 2013

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)

- João Araújo, James D. Mitchell
- The American Mathematical Monthly
- 2005

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)

- João Araújo, Paul von Bünau, James D. Mitchell, Max Neunhöffer
- J. Symb. Comput.
- 2010

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)

- João Araújo, Mário J. Edmundo, Steven Givant
- IJAC
- 2011

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)

- Lara Aires, João Araújo, António Dourado
- IFSA/EUSFLAT Conf.
- 2009

— 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)

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)

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal… (More)

- João Araújo, Peter J. Cameron
- J. Comb. Theory, Ser. B
- 2014

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)

- João Araújo, Michael K. Kinyon, Janusz Konieczny
- Eur. J. Comb.
- 2011

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)