In computability theory and computational complexity theory [Computational complexity theory], a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm 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 problem
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“Decision Problem.” 2023. Wikipedia, January. https://en.wikipedia.org/w/index.php?title=Decision_problem&oldid=1135637021.