Berechnungstheorie

Berechnungstheorie, also known as theory of computation, is a branch of theoretical computer science and mathematics that deals with what problems can be solved by computation, how efficiently they can be solved, and what models of computation are suitable for solving them. It is fundamentally concerned with the limits of computation and the capabilities of computers.

The field is typically divided into three main areas: automata theory and formal languages, computability theory, and computational complexity theory. Automata theory studies abstract machines called automata and the computational problems they can solve, as well as the formal languages they can recognize. Computability theory investigates which problems are solvable by an algorithm or a computer program, regardless of the resources required. This area explores the concept of an algorithm and what it means for a problem to be decidable or undecidable. Computational complexity theory, on the other hand, focuses on classifying problems according to their inherent difficulty and the amount of resources, such as time and space (memory), required to solve them. It seeks to understand the efficiency of algorithms and distinguish between problems that can be solved quickly and those that are computationally intractable.

Berechnungstheorie provides the foundational principles for many areas of computer science, including algorithm design, programming language theory, artificial intelligence, and cryptography. It helps us understand the fundamental capabilities and limitations of computing, guiding the development of new technologies and the design of more effective computational solutions.