RE denoted the family of Turing computable sets of vectors generated by arbitrary grammars.
2.
There are Turing computable partial functions that have no extension to a total Turing computable function.
3.
There are Turing computable partial functions that have no extension to a total Turing computable function.
4.
If a Turing machine can complete the task, it is considered Turing computable or more commonly, Turing complete.
5.
Existing quantum computers are only capable of reducing the complexity of Turing computable tasks and are still restricted to tasks within the scope of Turing machines.
6.
Gandy states that " the functions which can be calculated by ( 1 ), ( 2 ), and ( 4 ) are precisely those which are Turing computable . " ( p . 53 ).
7.
Church and Turing proved that these three formally defined classes of computable functions coincide : a function is ?-computable if and only if it is Turing computable if and only if it is " general recursive ".
8.
To establish that a function is computable by Turing machine, it is usually considered sufficient to give an informal English description of how the function can be effectively computed, and then conclude " by the Church Turing thesis " that the function is Turing computable ( equivalently, partial recursive ).
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