invalidate the ChurchâTuring thesis.
The Church-Turing thesis is a statement of type 2.
There are various equivalent formulations of the Church-Turing thesis.A common one is that every effective computation can be carried out bya Turing machine. The Church-Turing thesis is often misunderstood,particularly in recent writing in the philosophy of mind.
Now, applying Gödel’s completeness theorem to this yieldsin turn:
Some of the philosophical questions raised by the theory of quantum computation are discussed. First it is considered whether the possibility of exponential speed-up in quantum computation provides an argument for a more substantive notion of quantum information than so far allowed. It is concluded that this is not so. Then some questions regarding the status of the Church-Turing hypothesis in the light of quantum computation are considered. In particular, Deutsch’s claim that a physical principle, the Turing Principle, underlies the Church-Turing hypothesis is rebutted. Finally, the question of whether the Church-Turing hypothesis might serve as a constraint on the laws of physics is briefly considered.
What would it mean to disprove Church-Turing thesis?
Since it can also be shown that there are no functions in other than ones whose values can be obtained by a methodsatisfying the above conditions for effectiveness, the Church-Turingthesis licences replacing the informal claim “There is aneffective method for obtaining the values of function ”by the formal claim “ is a member of”—or by any other formal claim equivalent to thisone.
Church Turing Thesis - SlideShare
In the Church–Turing thesis (also known as the Church-Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a combined ("thesis") about the nature of (computable) functions by (Church's Thesis), by mechanical device equivalent to a (Turing's Thesis) or by use of Church's . The three computational processes (recursion, λ-calculus, and Turing machine) were shown to be equivalent by , , (1934–6) and (1936–7).
Church-Turing thesis - Psychology Wiki
Informally the Church–Turing thesis states that if an (a procedure that terminates) exists then there is an equivalent , -definable function, or , for that algorithm. A more simplified but understandable expression of it is that "everything computable is computable by a Turing machine." Though not formally proven, today the thesis has near-universal acceptance.