The filter generator consists of a linear feedback shift register (LFSR) and a Boolean filtering function that combines bits from the shift register to create a key stream. The nonlinear combiner generator employs several (LFSRs) and a Boolean function that combines bit from all the registers to generate the key stream. A new attack on the filter generator has recently been described by Rønjom ...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

Proof-search (the basis of logic programming) with multiplicative inference rules, such as linear logic's R and OL, is problematic because of the required non-deterministic splitting of resources. Similarly , searching with additive rules such as NL and R requires a non-deterministic choice between two formulae. Many strategies which resolve such non-determinism, either locally or globally, are...

In this paper, we present related quantum algorithms to check the order of resiliency, symmetry and linearity of a Boolean function that is available as a black-box (oracle). First we consider resiliency and show that the Deutsch-Jozsa algorithm can be immediately used for this purpose. We also point out how the quadratic improvement in query complexity can be obtained over the DeutschJozsa alg...

This paper is concerned with the problem of Boolean approximation in the following sense: given a Boolean function class and an arbitrary Boolean function, what is the function’s best proxy in the class? Specifically, what is its strongest logical consequence (or envelope) in the class of affine Boolean functions. We prove various properties of affine Boolean functions and their representation ...

We exploit the “regularity” of Boolean functions with the purpose of decreasing the time for constructing minimal threelevel expressions, in the sum of pseudoproducts (SPP) form recently developed. The regularity of a Boolean function of variables can be expressed by an autosymmetry degree (with 0 ). = 0 means no regularity, that is we are not able to provide any advantage over standard synthes...

In this paper, we consider a subclass of the Maiorana–McFarland class used in the design of resilient nonlinear Boolean functions. We show that these functions allow a simple modification so that resilient Boolean functions of maximum algebraic degree may be generated instead of suboptimized degree in the original class. Preserving a high-nonlinearity value immanent to the original construction...

This paper concerns the open problem of Lovasz and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We rst give an example exhibiting the largest gap known. We then prove two related theorems. y Extended Abstract appeared in FOCS 1994. subject "MAIL ME CLEAR", body "pub/eccc/ftpmail.txt" followed by an empty line, ...

In Boolean algebra, true statements are denoted 1 and false statements are denoted 0. A Boolean function acts on a set of these Boolean values and outputs a set of Boolean values (usually just one). The most common Boolean operators used are NOT, AND, OR, and XOR. 2.1 NOT NOT is a Boolean function that takes in one Boolean value and outputs its negation. Let x be a Boolean variable. NOT(x) is d...

We find a simple linear relation between the thermodynamic entropy and the largest Lyapunov exponent (LLE) of an discrete hydrodynamical system, a deterministic, two-dimensional lattice gas automaton (LGCA). This relation can be extended to irreversible processes considering the Boltzmann’s H function and the expansion factor of the LLE. The definition of LLE for cellular automata is based on t...