The Church-Turing thesis posits that a function on the natural numbers is effectively calculable if and only if it is computable by a Turing machine. It is named after the American mathematician Alonzo Church and the British mathematician Alan Turing. Church, along with Kleene and Turing, demonstrated that three formally defined classes of computable functions are equivalent: a function is λ-computable if and only if it is Turing computable, and if and only if it is generally recursive. This convergence has led to the widely held belief that these three equivalent processes accurately characterize computability. However, the Church-Turing thesis itself cannot be formally proven, as the concept of effective calculability is not formally defined.
The P vs. NP problem is one of the Millennium Prize Problems-seven unsolved mathematical challenges with a $1 million prize for each solution.
The Church-Turing thesis posits that a function on the natural numbers is effectively calculable if and only if it is computable by a Turing machine. It is named after the American mathematician Alonzo Church and the British mathematician Alan Turing. Church, along with Kleene and Turing, demonstrated that three formally defined classes of computable functions are equivalent: a function is λ-computable if and only if it is Turing computable, and if and only if it is generally recursive. This convergence has led to the widely held belief that these three equivalent processes accurately characterize computability. However, the Church-Turing thesis itself cannot be formally proven, as the concept of effective calculability is not formally defined.
The Genie has "intuition" = intuition into a complex information (e.g. a proof) takes no time, it's instantaneous (Penrose).
Where is the QuantumCloud.
The law of Physics is submath.