<P> In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes - no question of the input values . 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 . </P> <P> For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem . The answer can be either' yes' or' no', and depends 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, given x and y . One such algorithm is long division, taught to many school children . If the remainder is zero the answer produced is' yes', otherwise it is' no' . A decision problem which can be solved by an algorithm, such as this example, is called decidable . </P>

What are the characteristics of a decision problem
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