Definition:Computational Method/Computational Sequence

Definition

Consider the computational method $\left({Q, I, \Omega, f}\right)$ in which:

$Q$ represents the set of states of the computation

$I$ represents the input to the computation

$\Omega$ represents the output from the computation

$f: Q \to Q$ represents the computational rule

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

$x_0 = x$

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

A computational sequence $x_0, x_1, x_2, \ldots$ is said to terminate in $k$ steps if $k$ is the smallest integer for which $x_k \in \Omega$.

In this case, it produces the output $x_k$ from $x$.