Information Processing Letters
Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
Disjunctive normal forms of Boolean functions with a small number of zeros
USSR Computational Mathematics and Mathematical Physics
Boolean functions with engineering applications and computer programs
Boolean functions with engineering applications and computer programs
A Spectral Lower Bound Technique for the Size of Decision Trees and Two-Level AND/OR Circuits
IEEE Transactions on Computers
USSR Computational Mathematics and Mathematical Physics
On the necessity of Occam algorithms
Theoretical Computer Science
Learning with malicious membership queries and exceptions (extended abstract)
COLT '94 Proceedings of the seventh annual conference on Computational learning theory
An introduction to computational learning theory
An introduction to computational learning theory
Malicious Omissions and Errors in Answers to Membership Queries
Machine Learning
Exact learning of DNF formulas using DNF hypotheses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Information Processing Letters
The Minimum Equivalent DNF Problem and Shortest Implicants
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Horn complements: towards horn-to-horn belief revision
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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Given a disjunctive normal form (DNF) expression ϕ and a set A of vectors satisfying the expression, called the set of exceptions, we would like to update ϕ to get a new DNF which is false on A, and otherwise is equivalent to ϕ. Is there an algorithm with running time polynomial in the number of variables, the size of the original formula and the number of exceptions, which produces an updated formula of size bounded by a certain type of function of the same parameters?We give an efficient updating algorithm, which shows that the previously known best upper bound for the size of the updated expression is not optimal in order of magnitude. We then present a lower bound for the size of the updated formula in terms of the parameters, which is the first known lower bound for this problem. We also consider the special case (studied previously in the complexity theory of disjunctive normal forms) where the initial formula is identically true, and give efficient updating algorithms, providing new upper bounds for the size of the updated expression.