Computational Theory Questions Medium
The Church-Turing thesis is a hypothesis in the field of computational theory that states that any function that can be effectively computed by an algorithm can also be computed by a Turing machine. In simpler terms, it suggests that any problem that can be solved by an algorithm can also be solved by a Turing machine.
The thesis was proposed independently by mathematician Alonzo Church and logician Alan Turing in the 1930s. Church formulated his thesis in terms of lambda calculus, a formal system for expressing computation, while Turing described it in terms of his theoretical machine, now known as the Turing machine.
The Church-Turing thesis has significant implications for the field of computer science and the study of computation. It implies that any problem that can be solved algorithmically has a corresponding Turing machine that can solve it. This thesis forms the foundation of modern computer science and helps establish the limits of what can be computed.
However, it is important to note that the Church-Turing thesis is a hypothesis and has not been proven formally. It is widely accepted due to the consistency of its predictions with real-world computation, but it remains an open question whether there are any computational models beyond the scope of the thesis.