Related papers: Boolean derivatives and computation of cellular au…
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e.…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
Generation of pseudo random sequences by cellular automata, as well as by hybrid cellular automata is surveyed. An application to the fast evaluation and FPGA implementation of some classes of boolean functions is sketched out.
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger)…
We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy…
The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…