On irreversibility of von Neumann additive cellular automata on grids

Nonlinear $*$-Lie higher derivations on factor von Neumann algebras

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.

Chebyshev polynomials over finite fields and reversibility of -automata on square grids

Using number theory on function fields and algebraic number fields we prove results about Chebyshev polynomials over finite prime fields to investigate reversibility of two-dimensional additive cellular automata on finite square grids. For example, we show that there are infinitely many primitive irreversible additive cellular automata on square grids when the base field has order two or three.

Signal crossing solutions in von Neumann self-replicating cellular automata

Signal crossing is a significant problem within von Neumann cellular automata (29-states); only three solutions are known. This paper gives a thorough examination of these three solutions, including discussion of performance and the effective means of construction, including the mechanism of autoinitialisation. Application of these solutions within self-replicators is then examined for Nobili a...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

The Cryptographic Properties of Von Neumann Cellular Automata

In this paper it is shown that two-dimensional cellular automata with Von Neumann neighborhoods are not suitable for cryptographic purposes. This result is obtained after analyzing the most important cryptographic properties of boolean functions defining their local transition rules 2000 Mathematics Subject Classifications: 68Q80, 94A60, 94C10