A 3D computer assisted Orthopedic Surgery Planning approach based on planar radiography

Dissertação de mestrado integrado em Engenharia Biomédica (área de especialização em Informática Médica)

Hand gesture recognition system based in computer vision and machine learning

"Lecture notes in computational vision and biomechanics series, ISSN 2212-9391, vol. 19"

Factoriality and the pin-reutenauer procedure

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.