Computational Complexity Theory

Computational Complexity Theory studies the resources needed to solve problems, particularly the time and space required based on problem size. It classifies problems into categories, such as those that can be solved quickly (in polynomial time) or those that are inherently difficult (non-deterministic polynomial time or NP problems). This field intersects with Model Theory and Computability Theory, which explore the limits of computation and formal systems. Together, they help us understand what can be computed, how efficiently, and the theoretical boundaries of algorithms and problems in mathematics and computer science.