Algebra and logic. Some problems

The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems are distributed in the corresponding parts. The whole material oriented towards universal algebraic geometry (UAG), i.e., geometry in an arbitrary variety of algebras $\Theta$. We consider logical geometry (LG) as a part of UAG. This theory is strongly influenced by model theory and ideas of A.Tarski and A.I.Malcev

A pattern language for parallelizing irregular algorithms

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia InformáticaIn irregular algorithms, data set’s dependences and distributions cannot be statically predicted. This class of algorithms tends to organize computations in terms of data locality instead of parallelizing control in multiple threads. Thus, opportunities for exploiting parallelism vary dynamically, according to how the algorithm changes data dependences. As such, effective parallelization of such algorithms requires new approaches that account for that dynamic nature. This dissertation addresses the problem of building efficient parallel implementations of irregular algorithms by proposing to extract, analyze and document patterns of concurrency and parallelism present in the Galois parallelization framework for irregular algorithms. Patterns capture formal representations of a tangible solution to a problem that arises in a well defined context within a specific domain. We document the said patterns in a pattern language, i.e., a set of inter-dependent patterns that compose well-documented template solutions that can be reused whenever a certain problem arises in a well-known context