Komponenta výukového serveru TI - P-úplné problémy

Abstract

This bachelor’s thesis focuses on the design and practical implementation of an educational tool centered on P-complete problems within theoretical computer science. The introductory part pro- vides a theoretical analysis of complexity classes, specifically focusing on class P , the definition of P-completeness, and the principles of log-space reductions. The thesis covers the Monotone Circuit Value Problem (MCVP) in detail, along with the mechanism for transforming general logic circuits into monotone ones using De Morgan’s laws. For the practical part, I developed a dynamic web application using .NET Blazor. I implemented the control logic to visualize how MCVP instances are reduced to other P-complete problems, specifically context-free grammars and the composition of algebraic operations. The result is a functional educational website that shows students how these transformations work step-by-step.