Search Problems - Introduction

Learn about existential theorems and search problems in computational complexity theory through this 2-hour seminar lecture. Explore how existential theorems demonstrate that for every object of a particular type (such as a mapping from a large set to a small set), there exists a related object (like a collision). Discover the relationships between different theorems through reductions, including how the Brouwer fixed point theorem can be reduced to Sperner's lemma. Examine these reductions in both computational complexity and decision tree settings, gaining insight into fundamental concepts that bridge theoretical computer science and mathematical logic.