Horn Minimization

This document is a report of a master thesis made at HSE computer science faculty (Moscow). It has been conducted in the context of a double-diploma program with the ISIMA (France). The topic was implication theories, or Horn, minimization, used in database applications for instance. More precisely the aim was to provide a review of existing algorithms for performing minimization and implement them to see how do they behave under practical test cases. By the end of the period, we found several algorithms and reviewed them within the context of closure systems. On top of providing explanations on their operation and complexity analysis, we implemented those algorithms using C++. Using randomly generated systems as real data, we determined which closure operator matches the best each algorithm and which algorithm or steps are likely to be used in practice. Those results being valid within the context of our experiments, suggest further research and experiments to lead in future work. Keywords: theoretical computer science, implications, closure systems, minimization, canonical basis, algorithmic.