The sequences produced by the cryptographic sequence generator known as the shrinking generator can be modelled as the output sequences of linear elementary cellular automata. These sequences are composed of interleaved m-sequences produced by linear structures based on feedback shifts. This profitable characteristic can be used in the cryptanalysis of this generator. In this work we propose an...

This elucidation studies ergodicity and equilibrium measures for additive cellular automata with prime states. Additive cellular automata are ergodic with respect to Bernoulli measure unless it is either an identity map or constant. The formulae of measure-theoretic and topological entropies can be expressed in closed forms and the topological pressure is demonstrated explicitly for potential f...

If A = Z/2, then A Z is a compact abelian group. A linear cellular automaton is a shift-commuting endomorphism Φ of A. If μ is a probability measure on A, then Φ asymptotically randomizes μ if Φjμ converges to the Haar measure as j→∞, for j in a subset of Cesàro density one. Via counterexamples, we show that nonzero entropy of μ is neither necessary nor sufficient for asymptotic randomization. ...

Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper, we investigate the ability of cellular automata related to functional computation. We introduce several functional classes of low time complexity which conta...

De Bruijn graphs provide a convenient way to describe configura tions of linear cellular automata (CAs). Using these graphs, we give a simple quadra tic time algorithm to determine whether a linear CA is reversible. Similarly, one can decide in quadratic time whether the global map of the auto mato n is surjective. We also show that every recursive configuration that has a predecessor on a line...

We study computational properties of linear cellular automata on configurations that differ from spatially periodic ones in only finitely many places. It is shown that the degree structure of the orbits of cellular automata is the same on these configurations as on the space of finite configurations. We also show that it is undecidable whether the cellular automaton exhibits complicated behavio...

Sorting is one of the fundamental problems in computer science and being used vastly in various domains. So different serial and parallel approaches have been proposed. One of the parallel sorting methods are algorithms that are based on computational model of cellular automata. A cellular automata machine is a structure of interconnected elementary automata evolving in a parallel and synchrono...

Let V be a finite-dimensional vector space over a field K and let G be a sofic group. We show that every injective linear cellular automaton τ : V G → V G is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result previously established by G. Elek and A. Szabó using different methods.

We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata’s computational power. The configurations we consider have finite but unbounded size.