Definition and Properties of Algorithm
14. Definition and Properties of Algorithm
In Webster's dictionary, the word "Algorithm" is defined as "any special
method of solving a certain kind of problem". But in computer science it
has a special meaning. It means a step by step procedure for solving a
problem by a computer. An algorithm has following properties.
1. An algorithm must be composed of a finite number of steps. Each
step may be another algorithm composed of several steps.
2. Each step of the algorithm must be definite. The meaning of the
operation must be clear. We cannot have an operation like "add 2 or
3 to x" in an algorithm.
3. The steps must be effective; each step can at least in principle be
done by a person using pencil and paper in finite amount of time.
Performing arithmetic on integers is an example of an effective
operation, but arithmetic with real numbers is not necessarily
effective, since some values may be expressible only by an infinitely
long decimal expression
4. The algorithm may have one or more inputs but it must have at least
one output.
5. An algorithm must terminate after a finite number of operations.
There is another word for an algorithm which obeys all of the above
properties except termination, and that is computational procedure.
An operating system of a digital computer is an example of a
computational procedure since it does not terminate, but continues in
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