# Learning *k*-term monotone Boolean formulae

## Abstract

Valiant introduced a computational model of learning by examples, and gave a precise definition of learnability based on the model. Since then, much effort has been devoted to characterize learnable classes of concepts on this model. Among such learnable classes is the one, denoted *k*-term MDNF, consisting of monotone disjunctive normal form formulae with at most *k* terms. In literature, *k*-term MDNF is shown to be learnable under the assumption that examples are drawn according to the uniform distribution. In this paper we generalize the result to obtain the statement that *k*-term MDNF is learnable even if positive examples are drawn according to such distribution that the maximum of the ratio of the probabilities of two positive examples is bounded from above by some polynomial.

## Keywords

Boolean Function Target Function Learnable Classis Boolean Formula Disjunctive Normal Form## Preview

Unable to display preview. Download preview PDF.

## References

- [1]Gu, Q. P. and Maruoka, A., Learning Monotone Boolean Functions by Uniformly Distributed Examples,
*SIAM Journal on Computing*, to appear.Google Scholar - [2]Kearns, M., Li, M., Pitt, L. and Valiant, L. G., On the Learnability of Boolean Formulae,
*In proceedings of the 19th Annual ACM Symposium on Theory of Computing*, 1987, pp.285–295.Google Scholar - [3]Kucera, L., Marchetti-Spaccamela, A. and Protasi, M., On the learnability of DNF formulae,
*Lecture Notes in Computer Science*, 1988, 317:347–361.Google Scholar - [4]Ohguro, T. and Maruoka, A., A learning algorithm for monotone
*k*-term DNF,*Proceeding of FUJITSU IIAS-SIS Workshop on Computational Learning Theory*, 1989.Google Scholar - [5]Valiant, L. G., A theory of the learnable,
*Communications of the ACM*, 27(11), 1984, pp.1134–1142CrossRefGoogle Scholar