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:
“I promise you, but for your company,
I would have been a-bed an hour ago.”
—William Shakespeare (1564–1616)
“Our young people are diseased with the theological problems of original sin, origin of evil, predestination, and the like. These never presented a practical difficulty to any man,—never darkened across any man’s road, who did not go out of his way to seek them. These are the soul’s mumps, and measles, and whooping- coughs, and those who have not caught them cannot describe their health or prescribe a cure. A simple mind will not know these enemies.”
—Ralph Waldo Emerson (1803–1882)