Formal Definition
A decision problem can be associated with a language, where the problem is to accept all inputs in and reject all inputs not in . For a promise problem, there are two languages, and, which must be disjoint, which means, such that all the inputs in are to be accepted and all inputs in are to be rejected. The set is called the promise. There are no requirements on the output if the input does not belong to the promise. If the promise equals, then this is also a decision problem, and the promise is said to be trivial.
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