Decision problem facts for kids

A decision problem is a problem that can be posed as a yes-no question of the input values. It is a type of problem in mathematics. An example of a decision problem is deciding whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem. A decision procedure for the decision problem "given two numbers x and y, does x evenly divide y?" would give the steps for determining whether x evenly divides y. One such algorithm is long division. If the remainder is zero the answer is 'yes', otherwise it is 'no'. A decision problem which can be solved by an algorithm is called decidable.

Decision problems typically appear in mathematical questions of decidability, that is, the question of the existence of an effective method to determine the existence of some object or its membership in a set; some of the most important problems in mathematics are undecidable.