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:
“As the saffron tints and crimson flushes of morn herald the coming day, so the social and political advancement which woman has already gained bears the promise of the rising of the full-orbed sun of emancipation. The result will be not to make home less happy, but society more holy.”
—Frances Ellen Watkins Harper (1825–1911)
“Most childhood problems don’t result from “bad” parenting, but are the inevitable result of the growing that parents and children do together. The point isn’t to head off these problems or find ways around them, but rather to work through them together and in doing so to develop a relationship of mutual trust to rely on when the next problem comes along.”
—Fred Rogers (20th century)