ChurchTuringteorien

Church-Turing theory, often referred to as the Church-Turing thesis, is a foundational concept in the theory of computation. It concerns the formalization of what it means for a function to be computable and the limits of mechanical calculation.

In the 1930s, Alonzo Church introduced the lambda calculus as a formal model of computation, while Alan Turing proposed the abstract Turing machine. Later work by researchers such as Kleene and others showed that lambda calculus, Turing machines, and recursive function theory all capture the same class of computable functions. This alignment across distinct formal systems is central to the formal notion of computability.

The central claim is that these standard models characterize the same set of computable functions. This equivalence is often treated as a theorem about computability. The Church-Turing thesis extends this idea to the intuitive notion of what can be calculated by a human following a finite sequence of steps, suggesting that any effectively calculable procedure can be performed by one of these formal machines.

The thesis is not a formal mathematical theorem; rather, it is a philosophical and empirical claim about the reach of formal models. It is widely accepted but discussed in light of developments such as quantum computing, probabilistic machines, and potential hypercomputation, which some argue could transcend traditional models.

Its influence on computer science is profound. It underpins the concept of universal computation, explains why digital computers are capable general-purpose devices, and clarifies why certain problems are undecidable (such as the halting problem) while others are decidable.