More specifically, let be a set of words in a given alphabet and let be a function which maps elements of to words on the same alphabet. We say that is Turing computable if there exists a Turing machine such that
If one starts the Turing machine with a word as the initial content of the tape, the computation will halt.
When the computation halts, the tape will read .
Formally, let be an alphabet and on words over . Then is said to be Turing-computable if there is a Turing machine over (its input alphabet), as defined in this entry (http://planetmath.org/FormalDefinitionOfATuringMachine), such that for any ,
for some . Here, is a halt state (either an accept or a reject state), and for any word is defined as the tape description such that the content of the -th square is the -th letter of , and blank everywhere else.
Because of the fact that all types of Turing machines (deterministic, non-deterministic, single head, multiple head, etc.) all have the same computational power, it does not matter which type of Turing machine one uses in the definition.
It is not hard to find examples of Turing computable functions — because Turing machines provide an idealized model for the operation of the digital computer, any function which can be evaluated by a computer provides an example.
|Date of creation||2013-03-22 12:33:16|
|Last modified on||2013-03-22 12:33:16|
|Last modified by||rspuzio (6075)|