ChurchTuringtétel

The Church-Turing thesis is a fundamental hypothesis in the theory of computation. It proposes that any function that can be computed by an algorithm can be computed by a Turing machine. A Turing machine is a theoretical model of computation that consists of a tape, a head that can read and write symbols on the tape, and a set of rules. The thesis also suggests that any physically realizable computing device is equivalent in computational power to a Turing machine.

This thesis was independently formulated by Alonzo Church and Alan Turing in the 1930s. Church developed a formal system called the lambda calculus, which he showed could compute a class of functions. Turing, on the other hand, introduced the concept of the Turing machine, a more mechanical model of computation. They later proved that their respective models were computationally equivalent, meaning they could compute the same set of functions.

The Church-Turing thesis is not a mathematical theorem that can be proven, as it makes a claim about the nature of computation itself. Instead, it is a widely accepted principle based on the evidence that all proposed models of computation have been shown to be equivalent to Turing machines. It has significant implications for computer science, forming the basis for understanding the limits of what can be computed and the design of programming languages and computer architectures.