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 $$\Omega \subseteq Q$$;
 * $$\forall x \in \Omega: f \left({x}\right) = x$$.

Each $$x \in I$$ defines a computational sequence $$x_0, x_1, x_2, \ldots$$ as follows:
 * $$x_0 = x$$;
 * $$\forall k \ge 0: x_{k+1} = f \left({x_k}\right)$$.

The computational sequence 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 $$x$$.

Some computational sequences may never terminate.

An algorithm is a computational method which terminates in finitely many steps for all $$x \in I$$.

Historical Note
This definition is very nearly the same as that given by A.A. Markov, Jr. in his Theory of Algorithms (1954).