Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In this paper, by using the relationship between some flats and support of a n variables Boolean function f , we introduce a general method to determine the algebraic immunity of a Boolean function and finally construct some balanced functions with optimum algeb...

We consider the problem of evaluating a Boolean function on PRAMs. We exhibit a Boolean function f : {0, 1} → {0, 1} that can be evaluated in time O(log log n) on a deterministic CROW (Concurrent Read Owner Write) PRAM, but requires time Ω(log n) on EROW (Exclusive Read Owner Write) PRAMs. Our lower bound also holds for randomized Monte Carlo EROW PRAMs. This Boolean function is derived from th...

Data structures for Boolean functions build an essential component of design automation tools, especially in the area of logic synthesis. The state of the art data structure is the ordered binary decision diagram (OBDD), which results from general binary decision diagrams (BDDs), also called branching programs, by ordering restrictions. In the context of EXOR-based logic synthesis another type ...

We exhibit links between pseudo-Boolean optimization, graph theory and logic. We show the equivalence of maximizing a pseudo-Boolean function and finding a maximum weight stable set; symmetrically minimizing a pseudo-Boolean function is shown to be equivalent to solving a weighted satisfiability problem.

In this paper we use the support of a Boolean function to establish some algebraic properties. These properties allow us to obtain the degree of a Boolean function without having to calculate its algebraic normal form. Furthermore, we derive some algorithms and compute the average time to obtain the degree of some Boolean functions from its support.

It is well known that free Boolean algebra on n generators isomorphic to the of functions variables. The distributive lattice monotone In this paper we introduce concept De Morgan function and prove Keywords: Antichain, function, algebra.

1. Closed ideals. (1.1) Definition. Let 5 be an arbitrary set, and 2 a Boolean ring of subsets of 5. The algebra B(S, 2) consists of all uniform limits of finite linear combinations of characteristic functions of sets in 2. The norm in B(S, 2) is given by the formula ||/|| =SupseS \f(s) | • This definition is slightly more general than that given in [l ] where 2 is required to be a field of set...

We give an adaptive algorithm which tests whether an unknown Boolean function f : {0, 1} → {0, 1} is unate, i.e. every variable of f is either non-decreasing or non-increasing, or ε-far from unate with one-sided error using Õ(n/ε) queries. This improves on the best adaptive O(n/ε)-query algorithm from Baleshzar, Chakrabarty, Pallavoor, Raskhodnikova and Seshadhri [BCP17b] when 1/ε n. Combined w...

It is well known that Exclusive Sum-Of-Products (ESOP) expressions for Boolean functions require on average the smallest number of cubes. Thus, a simple complexity measure for a Boolean function is the number of cubes in its simplest ESOP. It will be shown that this structure-oriented measure of the complexity can be improved by a unique complexity measure which is based on the function. Thus, ...