Church–Turing thesis what can be computed is invalid". They claim that forms of computation not captured by the thesis are relevant today, terms which they call super-Turing computation. Philosophers have interpreted the Church–Turing thesis as having implications for the philosophy of mind. B. Jack Copeland states that it is an open empirical question whether there are actual deterministic physical processes that, in the long run, elude simulation by a Turing machine; furthermore, he states that it is an open empirical question whether any such processes are involved in the working of the human brain. There are also some important open questions which
Turing completeness is that there exist problems for which it is impossible to predict what a (Turing-complete) system will do over an arbitrarily long time. The classic example is the halting problem: create an algorithm which takes as input (a) a program in some Turing-complete language, and (b) some data to be fed to "that" program; and which determines whether the program, operating on the input, will eventually stop or will continue forever. It is trivial to create an algorithm that can do this for "some" inputs, but impossible to do this in general. For any characteristic of the program's eventual output,