Read-Twice DNF Formulas Are Properly Learnable

Evaluation of DNF Formulas

We consider the Stochastic Boolean Function Evaluation (SBFE) problem for classes of DNF formulas. The SBFE problem for DNF formulas is a “sequential testing” problem where we need to determine the value of DNF formula on an initially unknown input x = (x1, ..., xn), when there is a cost ci associated with obtaining the value of xi, each xi is equal to 1 with known probability pi, and the xi ar...

Learning Talagrand DNF Formulas

Consider the following version of Talagrand’s probabilistic construction of a monotone function f : {0, 1} n → {0, 1}. Let f be an n-term monotone DNF formula where each term is selected independently and uniformly at random (with replacement) from the set of all n log n) possible terms of length log(n) over the first log(n) variables. Let us call such a DNF formula a Talagrand DNF formula. Thi...

Read Once DNF Leaner p ( n ) − term DNF

Extraction of Coverings as Monotone DNF Formulas

In this paper, we extend monotone monomials as large itemsets in association rule mining to monotone DNF formulas. First, we introduce not only the minimum support but also the maximum overlap, which is a new measure how much all pairs of two monomials in a monotone DNF formula commonly cover data. Next, we design the algorithm dnf cover to extract coverings as monotone DNF formulas satisfying ...

Evaluating 2-DNF Formulas on Ciphertexts

Let ψ be a 2-DNF formula on boolean variables x1, . . . , xn ∈ {0, 1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1, . . . , xn. In other words, given the encryption of the bits x1, . . . , xn, anyone can create the encryption of ψ(x1, . . . , xn). More generally, we can evaluate quadratic multi-variate poly...