Manipulation of Boolean functions has important applications in such fields as hardware verification, non-monotonic reasoning, and decision support. Most often, in such applications, the set of prime implicates/implicants of a large formula must be computed. Many algorithms have been proposed to compute the prime implicates of propositionalBoolean formulas, e.g. [4, 5]. Most of them assume that...

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.

We construct trace codes over Z4 by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new family of optimal two-weight codes over Z4.

A new neural network (NN) approach is proposed in this paper to estimate the Boolean function (BF) complexity. Large number of randomly generated single output BFs has been used and experimental results show good correlation between the theoretical results and those predicted by the NN model. The proposed model is capable of predicting the number of product terms (NPT) in the BF that gives an i...

In order to systematize existing results, we propose to analyze the learnability of boolean functions computed by an algebraically defined model, programs over monoids. The expressiveness of the model, hence its learning complexity, depends on the algebraic structure of the chosen monoid. We identify three classes of monoids that can be identified, respectively, from Membership queries alone, E...

In recent years, there has been a great interest in studying Boolean functions by studying their analogous Boolean trees (with internal nodes labeled by Boolean gates; leaves viewed as inputs to the Boolean function). Many of these investigations consider Boolean functions of n variables and m leaves. Our study is related but has a quite different flavor. We investigate the mean output Xn of a ...

In this work we give a non-trivial upper bound on the spectral norm of various Boolean predicates of the Diie-Hellman function. For instance, we consider every individual bit and arbitrary unbiased intervals. Combining the bound with recent results from complexity theory we can rule out the possibility that a Boolean function with a too small spectral norm can be represented by simple functions...

The problem of reconstructing the and-or expression of a monotone Boolean function starting from a fixed subset of its truth table is solved by adopting a proper algorithm, called Shadow Clustering (SC). It generates a collection of prime implicants by descending the portion of the diagram of the Boolean lattice (associated with the input domain) that lies beneath the available examples. Three ...

ROBDD's((2]) are a very popular datastructure for the representation and manipulation of boolean functions. They have tractable sizes for many boolean functions and come up with eecient algorithms for boolean operations. In the worst case however, size and time complexity grows exponentially when performing a polynomial number of operations. However, there are applications where an approximate ...

In the past twenty years, there were only a few constructions for Boolean functions with nonlinearity exceeding the quadratic bound 2n−1 − 2(n−1)/2 when n is odd (we shall call them Boolean functions with very high nonlinearity). The first basic construction was by Patterson and Wiedemann in 1983, which produced unbalanced function with very high nonlinearity. But for cryptographic applications...