# Definition:Computational Method

## Definition

A computational method is an ordered quadruple $\left({Q, I, \Omega, f}\right)$ in which:

$Q$ is a set representing the states of the computation
$I$ is a set representing the input to the computation
$\Omega$ is a set representing the output from the computation
$f: Q \to Q$ is a mapping representing the computational rule

subject to the following constraints:

$I \subseteq Q$ and $\Omega \subseteq Q$
$\forall x \in \Omega: f \left({x}\right) = x$

### Computational Sequence

Each $x \in I$ defines a computational sequence $x_0, x_1, x_2, \ldots$ as follows:

$x_0 = x$
$\forall k \ge 0: x_{k+1} = f \left({x_k}\right)$

## Historical Note

The definition provided here for computational method is very nearly the same as that given by Andrey Andreyevich Markov Jr. in his The Theory of Algorithms (1954).