Completeness in approximation classes
Information and Computation
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Theory refinement combining analytical and empirical methods
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Estimation of Dependences Based on Empirical Data: Springer Series in Statistics (Springer Series in Statistics)
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A knowledge-based system uses its database (a k a its "theory") to produce answers to the queries it receives. Unfortunately, these answers may be incorrect if the underlying theory is faulty Standard "theory revision" systems use a given set of "labeled queries" (each a query paired with its correct answer) to transform the given theory, by adding and/or deleting either rules and/or antecedents, into a related theory that is as accurate as possible. After formally defining the theory revision task and bounding its sample complexity, this paper addresses the task's computational complexity. It first proves that, unless P = NP, no polynomial time algorithm can identify the optimal theory, even given the exact distribution of queries, except in the most trivial of situations. It also shows that, except in such trivial situations, no polynomial-time algorithm can produce a theory whose inaccuracy is even close (i e, within a particular polynomial factor) to optimal. These results justify the standard practice of hill-climbing to a locally-optimal theory, based on a given set of labeled samples.