Note of Computational Model

1. Urm-computable Functions

　　URM is short for Unlimited Registermachine, which are a computation model conceived by Shepherdson & Sturgis.

The function f is urm-computable iff there exists a program that urm-computes F.

2. Recursive Functions

　　Partial Recursive Functions is a set of computable Functions defined by Gödel and Kleene in 1936.

As an example, Ackerman function defined as follow are a partial recursive Function, but not a primitive recursive function.

　　　　　　

A predicate is decidable iff it characteristic function is recursive.

3. Turing-computable Functions

The three fundamental components of a multi-tape Turing Machine is an Alphabet (a finite set of symbols ), a finite set of states and a Transfer Function.

The computation ability of a Turing machine does does vary with its size of alphabet, its number of tapes, or whether its T Apes is unidirectional or bidirectional.

It can be proved that: urm-computable Functions = Partial Recursive Functions = turing-computable Functions

4. Church ' s thesis

The intuitively and informally defined class of effectively computable partial functions coincide exactly with the class O F urm-computable functions.

References:

1. Cutland, Nigel. Computability:an Introduction to recursive function theory [M]. Cambridge:cambridge University Press, 1980

Note of Computational Model