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:
“You’re gonna take the rap and play along. You’re gonna make every exact move I tell you. If you don’t, I’ll kill you. And I’ll promise you one thing, it won’t be quick. I’ll break you first. You won’t be able to answer a telephone or open a door without thinking “This is it.” And when it comes, it still won’t be quick. And it won’t be pretty.”
—Geoffrey Homes (1902–1977)
“My problem lies in reconciling my gross habits with my net income.”
—Errol Flynn (1909–1959)