Hasil untuk "nlin.CG"

Seung Hyeon Mandy Hong, May Mei

We investigate Conway's Game of Life played on the Robinson triangle Penrose tiling. In this paper, we classify all four-cell still lifes.

Kotaro Sakata, Yuta Tanaka, Daisuke Takahashi

We propose a max-plus equation which includes Conway's Game of Life (GoL) as a special case. There are some special solutions to the equation which include and unify those to GoL. Moreover, the multi-value extension of GoL is derived from the equation and the behavior of solutions is discussed.

Norihito Toyota

In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced Wolfram\cite{wolfram} by the proposed means of the inverse ultra-discretization. We show that the behaviors of ECAs can be completely reproduced by numerically solving the obtained difference equations.

Marek Pietrow

A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities stabilize with time and form a discrete spectrum of values. The presented model may have some general aspects in common with a cellular automaton representation of a quantum system.

Theophanes E. Raptis

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 equivalent of superpotentials. The results justify the search for alternative analog models of computation and their possible physical connections.

Yuji Kaneko

We studied the rule 150 elementary cellular automaton in terms of the distribution of the spacings of the singular values of the matieces obtained from proper time evolutions patterns. The distribution has strong resembrance to that of the random matrices which is derived from Painlevé V equation. Some analytic results for the relative period of the ECS are also presented.

Petr Kůrka, Enrico Formenti, Alberto Dennunzio

This work considers a cellular automaton (CA) with two particles: a stationary particle $1$ and left-going one $\overline{1}$. When a $\overline{1}$ encounters a $1$, both particles annihilate. We derive asymptotic distribution of appearence of particles at a given site when the CA is initialized with the Bernoulli measure with the probabilities of both particles equal to $1/2$.

Vincent Nesme, Guillaume Theyssier

We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear ones. Following the approach introduced by the first author in an earlier paper, we develop proof techniques to tell whether some linear CA can simulate another linear CA. Besides rigorous proofs, the necessary condition for the simulation to occur can be heuristically checked via simple observations of typical space-time diagrams generated from finite configurations. As an illustration, we give an example of linear reversible CA which cannot simulate the identity and which is 'time-asymmetric', i.e. which can neither simulate its own inverse, nor the mirror of its own inverse.

Zan Pan

In this paper, a different perspective of constructing the CA models is proposed. Its kernel, the Local Symmetric Distribution Principle, relates to some fundamental concepts in physics, which maybe raise a wide interest. With a rich palette of configurations, this model also hints its capability of universal computation.

Thomas Worsch, Hidenosuke Nishio

A new fast (real time) sorter of binary numbers by one-dimensional cellular automata is proposed. It sorts a list of n numbers represented by k-bits each in exactly nk steps. This is only one step more than a lower bound.

Hala El-Saka, E. Ahmed, M. I. Shehata et al.

This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.

Sudhakar Sahoo, Pabitra Pal Choudhury

This paper proposes several algorithms and their Cellular Automata Machine (CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic boundary) and length of the CA n. It also discusses the novelty, hardware cost and the complexities of these algorithms.

Nino Boccara

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 on random directed graphs with constant out-degrees and evolve according to cellular automaton rules. For some families of rules, a few typical a priori unexpected results are presented.

Bruno Durand, Enrico Formenti, Georges Varouchas

Equicontinuity classification is a popular classification of cellular automata based on their dynamical behavior. In this paper we prove that most of its classes are undecidable.

Christopher L. Barrett, Harry Hunt, Madhav V. Marathe et al.

A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in [BR99] as a formal model for analyzing simulation systems. Here, we address the complexity of two basic problems and their generalizations for SDSs.Given an SDS $\mathcal{S}$ and a configuration $\mathcal{C}$, the PREDECESSOR EXISTENCE (or PRE) problem is to determine whether there is a configuration $\mathcal{C}'$ such that $\mathcal{S}$ has a transition from $\mathcal{C}'$ to $\mathcal{C}$. Our results provide separations between efficiently solvable and computationally intractable instances of the PRE problem. For example, we show that the PRE problem can be solved efficiently for SDSs with Boolean state values when the node functions are symmetric and the underlying graph is of bounded tree width. In contrast, we show that allowing just one non-symmetric node function renders the problem $\mathbf{NP}$-complete even when the underlying graph is a star (which has a tree width of 1). Our results extend some of the earlier results by Sutner [Su95] and Green [Gr87] on the complexity of the PREDECESSOR EXISTENCE problem for 1-dimensional cellular automata.Given two configurations $\mathcal{C}$ and $\mathcal{C}'$ of a partial SDS $\mathcal{S}$, the PERMUTATION EXISTENCE (or PME) problem is to determine whether there is a permutation of nodes such that $\mathcal{S}$ has a transition from $\mathcal{C}'$ to $\mathcal{C}$ in one step. We show that the PME problem is $\mathbf{NP}$-complete even when the function associated with each node is a simple-threshold function. We also show that the problem can be solved efficiently for SDSs whose underlying graphs are of bounded degree and bounded tree width. We consider a generalized version (GEN-PME) of the PME problem and show that the problem is $\mathbf{NP}$-complete for SDSs where each node function is NOR and the underlying graph has a maximum node degree of 3. When each node computes the OR function or when each node computes the AND function, we show that the GEN-PME problem is solvable in polynomial time.

Arnaud Dartois, Clémence Magnien

In this paper we study the identity of the Abelian Sandpile Model on a rectangular lattice.This configuration can be computed with the burning algorithm, which, starting from the empty lattice, computes a sequence of configurations, the last of which is the identity.We extend this algorithm to an infinite lattice, which allows us to prove that the first steps of the algorithm on a finite lattice are the same whatever its size.Finally we introduce a new configuration, which shares the intriguing properties of the identity, but is easier to study.

Nazim Fatès

Classifying cellular automata in order to capture the notion of chaos algorithmically is a challenging problem than can be tackled in many ways.We here give a classification based on the computation of a macroscopic parameter, the $d$-spectrum, and show how our classifying scheme can be used to separate the chaotic ECA from the non-chaotic ones.

A. Awazu

A cellular automaton named Rule 184++C is proposed as a meta-model to investigate the flow of various complex particles. In this model, unlike the granular pipe flow and the traffic flow, not only the free-jam phase transition but also the free-intermediate, the intermediate-jam, and the dilute-dense phase transitions appear. Moreover, the freezing phenomena appear if the system contains two types of different particles.

Luís Correia, Thomas Wehrle

Noise in the local transition function is compared to fluctuations in the updating times of the cells. Obtained results are shown to be quite different in both cases. In this extended abstract we briefly explain the problem and present results obtained and comment them.

J. Machta, K. Moriarty

The Lorentz lattice gas is studied from the perspective of computational complexity theory. It is shown that using massive parallelism, particle trajectories can be simulated in a time that scales logarithmically in the length of the trajectory. This result characterizes the ``logical depth" of the Lorentz lattice gas and allows us to compare it to other models in statistical physics.