komplexitáselméletet

Komplexitáselmélet (Complexity Theory) is a fundamental branch of theoretical computer science and mathematics that focuses on classifying computational problems based on their inherent difficulty. It seeks to understand the resources, such as time and memory, required to solve these problems using algorithms. The core idea is to distinguish between problems that are efficiently solvable and those that are not, even with the most powerful computers imaginable.

A key concept in complexity theory is the class P, which contains problems that can be solved by a deterministic Turing machine in polynomial time. Conversely, the class NP comprises problems for which a proposed solution can be verified in polynomial time by a deterministic Turing machine. The famous P versus NP problem, one of the most important unsolved problems in computer science, asks whether every problem in NP can also be solved in polynomial time (i.e., if P = NP). Most computer scientists believe that P ≠ NP, suggesting that there are problems whose solutions are easy to check but very hard to find.

Complexity theory also introduces other complexity classes, such as EXPTIME (problems solvable in exponential time) and PSPACE (problems solvable using polynomial space). These classifications help researchers understand the limits of computation and guide the development of efficient algorithms for practical applications. The study of complexity theory has profound implications for fields ranging from cryptography and artificial intelligence to operations research and theoretical physics.