Promise Problems
In computational complexity theory, it is usually implicitly assumed that any string in {0, 1}* represents an instance of the computational problem in question. However, sometimes not all strings {0, 1}* represent valid instances, and one specifies a proper subset of {0, 1}* as the set of "valid instances". Computational problems of this type are called promise problems.
The following is an example of a (decision) promise problem:
- "Given a graph G, determine if every independent set in G has size at most 5, or G has an independent set of size at least 10."
Here, the valid instances are those graphs whose maximum independent set size is either at most 5 or at least 10.
Decision promise problems are usually represented as pairs of disjoint subsets (Lyes, Lno) of {0, 1}*. The valid instances are those in Lyes ∪ Lno. Lyes and Lno represent the instances whose answer is yes and no, respectively.
Promise problems play an important role in several areas of computational complexity, including hardness of approximation, property testing, and interactive proof systems.
Read more about this topic: Computational Problem
Famous quotes containing the words promise and/or problems:
“On the death of a friend, we should consider that the fates through confidence have devolved on us the task of a double living, that we have henceforth to fulfill the promise of our friend’s life also, in our own, to the world.”
—Henry David Thoreau (1817–1862)
“The problems of this world are only truly solved in two ways: by extinction or duplication.”
—Susan Sontag (b. 1933)