Church Turing Thesis Any algorithmic procedure that can be carried out at all, by a human computer or a team of humans or an electronic computer, can be carried out by a TM. This statement usually referred to as Church’s thesis, or the Church-Turing thesis. It is not a mathematically precise statement that can be proved, because we do not have a precise definition of the term algorithmic procedure. Here is an informal summary of some of the evidence. Humans normally work with a two-dimensional sheet of paper. A TM tape could be organized so as to simulate two dimensions; one likely consequence would be that the TM would require more moves to do what a human could do in one. Various enhancements of the TM model have been suggested to make the operation more like that of a human computer, or more convenient & efficient. The multitape TM is an example. Other theoretical models includes abstract machines with two stacks or with a queue. Since the introduction of the Turing machine, no one has suggested any type of computation that ought to be included in the category of “algorithmic procedure” and cannot be implemented on a TM.
