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Malheiro, A. "On Finite Semigroup Cross-Sections and Complete Rewriting Systems." International Conference on Theoretical and Mathematical Foundations of Computer Science, TMFCS-08, Orlando, Florida, USA, July 7-10, 2008. 2008. 59-63. Abstract

In this paper we obtain a [finite] complete rewriting system defining a semigroup/monoid S, from a given finite
right cross-section of a subsemigroup/submonoid defined by a [finite] complete presentation. In the semigroup case the subsemigroup must have a right identity element which must also be part of the cross-section. In the monoid case the submonoid and the cross-section must include the identity of the semigroup. The result on semigroups allow us to show that if G is a group defined by a [finite] complete rewriting system then the completely simple semigroup M[G; I, J; P] is also defined by a [finite] complete rewriting system.

Malheiro, A. On trivializers and subsemigroups.. Semigroups and formal languages. Proceedings of the international conference in honour of the 65th birthday of Donald B. McAlister. Lisboa, Portugal, July 12–15, 2005.: Hackensack, NJ: World Scientific, 2007. Abstract

The aim of this paper is to develop the calculus of trivializers for subsemigroups. Given a finite presentation defining a semigroup S and a trivializer of the Squier complex of , we obtain an infinite trivializer of the Squier complex of a finite presentation defining a subsemigroup of S. Also, we give a method to find finite trivializers for special subsemigroups and hence to show that those subsemigroups have finite derivation type (FDT). An application of this method is given: we prove that if is a band of monoids having FDT, then so does Sα, for any α ∈Y.

Malheiro, A. "Finite derivation type for Rees matrix semigroups." Theor. Comput. Sci.. 355 (2006): 274-290. AbstractWebsite

This paper introduces the topological finiteness condition finite derivation type (FDT) on the class of semigroups. This notion is naturally extended from the monoid case. With this new concept we are able to prove that if a Rees matrix semigroup M[S;I,J;P] has FDT then the semigroup S also has FDT. Given a monoid S and a finitely presented Rees matrix semigroup M[S;I,J;P] we prove that if the ideal of S generated by the entries of P has FDT, then so does M[S;I,J;P]. In particular, we show that, for a finitely presented completely simple semigroup M, the Rees matrix semigroup M=M[S;I,J;P] has FDT if and only if the group S has FDT.

Malheiro, A. Finiteness conditions of semigroup presentations.. Eds. G. M. S. Gomes. University of Lisbon. Lisbon: University of Lisbon, 2006.
Malheiro, A. "Complete rewriting systems for codified submonoids." Int. J. Algebra Comput.. 15 (2005): 207-216. AbstractWebsite

Given a complete rewriting system R on X and a subset X0 of X+ satisfying certain conditions, we present a complete rewriting system for the submonoid of M(X;R) generated by X0. The obtained result will be applied to the group of units of a monoid satisfying H1 = D1. On the other hand we prove that all maximal subgroups of a monoid defined by a special rewriting system are isomorphic.

Malheiro, A. Presentations and complete rewriting systems for semigroups. (in Portuguese). Eds. G. M. S. Gomes. Faculty of Sciences of the University of Lisbon. Lisbon: University of Lisbon, 2001.