ABSTRACT
A computation is a process by which we proceed from some initially given objects by means of a fixed set of rules to obtain some final results. The initially given objects are called inputs; the fixed set of rules is called an algorithm; and the final results are called outputs. It is always supposed that there is at most one output; for a computation with k outputs can be thought of as k different computations with one output each. Recursion theory is, at least in its initial stages, the theory of computability. In particular, the first task of recursion theory is to give a rigorous mathematical definition of computable. An algorithm is set of rules for proceeding from the inputs to the output. The algorithm must specify precisely and unambiguously what action is to be taken at each step; and this action must be sufficiently mechanical that it can be done by a suitable computer.
