ReAlM - a system to manipulate relations

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not necessarily finite. When a relational product exists or the point axiom is given, we can represent the relation algebra by concrete binary relations between sets, which means the algebra may be seen as an algebra of Boolean matrices. However, it is not possible to represent every relation algebra. It is well known that the smallest relation algebra that is not representable has only 16 elements. Such an algebra can not be put in a Boolean matrix form.[15] In [15, 16] it was shown that every relation algebra R with relational sums and sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is given by the integral objects of R, and is, compared to R, much smaller. Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras using the matrix approach.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

Real-Time Automatic Object Classification and Tracking using Genetic Programming and NVIDIA R CUDA TM

Genetic Programming (GP) is a widely used methodology for solving various computational problems. GP's problem solving ability is usually hindered by its long execution times. In this thesis, GP is applied toward real-time computer vision. In particular, object classification and tracking using a parallel GP system is discussed. First, a study of suitable GP languages for object classification is presented. Two main GP approaches for visual pattern classification, namely the block-classifiers and the pixel-classifiers, were studied. Results showed that the pixel-classifiers generally performed better. Using these results, a suitable language was selected for the real-time implementation. Synthetic video data was used in the experiments. The goal of the experiments was to evolve a unique classifier for each texture pattern that existed in the video. The experiments revealed that the system was capable of correctly tracking the textures in the video. The performance of the system was on-par with real-time requirements.