In computational complexity theory, a promise problem is a generalization of a decision problem where the input is promised to belong to a subset of all possible inputs. Unlike decision problems, the yes instances (the inputs for which an algorithm must return yes) and no instances do not exhaust the set of all inputs. Intuitively, the algorithm has been promised that the input does indeed belong to set of yes instances or no instances. There may be inputs which are neither yes or no. If such an input is given to an algorithm for solving a promise problem, the algorithm is allowed to output anything.
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Famous quotes containing the words promise and/or problem:
“Legislators or revolutionaries who promise equality coupled with freedom are either phantasts or charlatans.”
—Johann Wolfgang Von Goethe (1749–1832)
“The problem of induction is not a problem of demonstration but a problem of defining the difference between valid and invalid
predictions.”
—Nelson Goodman (1906)