komplexitáselmélethez

Complexity theory, or komplexitáselmélet in Hungarian, is a field of computer science and mathematics that studies the resources, such as time and memory, required to solve computational problems. It seeks to understand the inherent difficulty of problems, classifying them into different complexity classes based on the efficiency of algorithms that can solve them. A central concept in complexity theory is the distinction between problems that can be solved efficiently, often referred to as "easy" problems, and those that are believed to be computationally intractable, or "hard" problems.

The P versus NP problem is arguably the most famous unsolved question in complexity theory. P represents the class of problems solvable in polynomial time by a deterministic Turing machine, meaning the time required grows relatively slowly with the size of the input. NP, on the other hand, represents problems where a proposed solution can be verified in polynomial time by a deterministic machine. Whether P is equal to NP is a question of immense importance, as it would imply that all problems whose solutions can be quickly checked can also be quickly solved.

Other important concepts include NP-completeness, which identifies the hardest problems in NP, and various complexity classes like EXPTIME (problems solvable in exponential time) and PSPACE (problems solvable with polynomial space). Complexity theory provides a framework for understanding the limits of computation and guides the development of efficient algorithms.