Exact Learning Boolean Functions via the Monotone Theory

Exact Learning Boolean Function via the Monotone Theory

We study the learnability of boolean functions from membership and equivalence queries. We develop the Monotone Theory that proves 1) Any boolean function is learnable in polynomial time in its minimal DNF size, its minimal CNF size and the number of variables n. In particular, 2) Decision trees are learnable. Our algorithms are in the model of exact learning with membership queries and unrestr...

2 Learning Monotone Boolean Functions

Last time we finished the discussion about KM algorithm and its application. We also covered sparse Fourier representations and k-juntas of parities. In the end we started to talk about learning monotone Boolean functions and influence of such functions. Today We will first finish discussion about learning monotone Boolean functions. Then we will also talk about learning k-juntas of halfspaces....

On Learning Monotone Boolean Functions

Abstract We consider the problem of learning monotone Boolean functions over under the uniform distribution. Specifically, given a polynomial number of uniform random samples for an unknown monotone Boolean function , and given polynomial computing time, we would like to approximate as well as possible. We describe a simple algorithm that we prove achieves error at most , improving on the previ...

Competitive learning of monotone Boolean functions

We apply competitive analysis onto the problem of minimizing the number of queries to an oracle to completely reconstruct a given monotone Boolean function. Besides lower and upper bounds on the competitivity we determine optimal deterministic online algorithms for the smallest problem instances.

On Learning Monotone Boolean Functions under the Uniform Distribution