A class of boolean functions with linear combinational complexity

Complexity of Linear Boolean Operators Complexity of Linear Boolean Operators

How to compute a linear Boolean operator by a small circuit using only unbounded fanin addition gates? Because this question is about one of the simplest and most basic circuit models, it has been considered by many authors since the early 1950s. This has led to a variety of upper and lower bound arguments—ranging from algebraic (determinant and matrix rigidity), to combinatorial (Ramsey proper...

A 2.5 n-Lower Bound on the Combinational Complexity of Boolean Functions

Consider the combinational complexity L(f) of Boolean functions over the basis fl={]'l]': {0, 1}2->{0, 1}}. A new method for proving linear lower bounds of size 2n is presented. we establish for a special sequence of functions [: {0, 1} "+2 g(n)+x-> {0, 1}: 2.5n <=L(f)<-6n. Also a trade-off result between circuit complexity and formula size is derived. 1. Introduction. The interest in lower bou...

Complexity of Boolean Functions

s of Presentation: Paul Beame: Time-Space Tradeoffs and Multiparty Communication Complexity 9 Beate Bollig: Exponential Lower Bounds for Integer Multiplication Using Universal Hashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Philipp Wölfel: On k-wise l-mixed Boolean Functions . . . . . . . . . . . . . . 10 Elizabeta Okol’nishnikova: On One Lower Bound for Branching Progra...

Some properties for a class of meromorphically multivalent functions with linear operator

‎Making use of a linear operator‎, ‎which is defined here by means of‎ ‎the Hadamard product (or convolution)‎, ‎we define a subclass‎ ‎$mathcal {T}_{p}(a‎, ‎c‎, ‎gamma‎, ‎lambda; h)$ of meromorphically‎ ‎multivalent functions‎. ‎The main object of this paper is to‎ ‎investigate some important properties for the class‎. ‎We also derive‎ ‎many results for the Hadamard roducts of functions belong...

The complexity of Boolean functions