Search results for "Cellular Automata"

MODELING THE SHRUB ENCROACHMENT IN THE NORTHERN CHIHUAHUAN DESERT GRASSLANDS WITH A CELLULAR AUTOMATA MODEL

2014

Special factors and the combinatorics of suffix and factor automata

2011

AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.

From deterministic cellular automata to coupled map lattices

2016

A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown to ex…

Modelling and simulation of several interacting cellular automata

2015

Cellular automata are used for modelling and simulation of many systems. In some applications, the system is formed by a set of subsystems that can be modelled separately, but, in such cases, the existence of interactions between these subsystems requires additional modelling and computer programming. In this paper we propose a modelling methodology for the simulation of a set of cellular automata models that interact with each other. The modelling methodology is described, together with an insight on implementation details. Also, it is applied to a particular cellular automata model, the Sanpile model, to illustrate its use and to obtain some example simulations.

A Tool for Implementing and Exploring SBM Models: Universal 1D Invertible Cellular Automata

2005

The easiest form of designing Cellular Automata rules with features such as invertibility or particle conserving is to rely on a partitioning scheme, the most important of which is the 2D Margolus neighborhood. In this paper we introduce a 1D Margolus-like neighborhood that gives support to a complete set of Cellular Automata models. We present a set of models called Sliding Ball Models based on this neighborhood and capable of universal computation. We show the way of designing logic gates with these models, propose a digital structure to implement them and finally we present SBMTool, a software development system capable of working with the new models.

Diagrammatic approach to cellular automata and the emergence of form with inner structure

2018

We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs in rule space to be classified according to their hierarchy of layers. Since the method is valid for any discrete operator and only depends on the alphabet size, the resulting conclusions, of general validity, apply to CAs in any dimension or order in time, arbitrary neighborhood ranges and topology. We provide several examples of the method, illustrating how it can be applied to the mathematical modeling of the emergence of order out of disorder. Specif…

Quantum versus Probabilistic One-Way Finite Automata with Counter

2001

The paper adds the one-counter one-way finite automaton [6] to the list of classical computing devices having quantum counterparts more powerful in some cases. Specifically, two languages are considered, the first is not recognizable by deterministic one-counter one-way finite automata, the second is not recognizable with bounded error by probabilistic one-counter one-way finite automata, but each recognizable with bounded error by a quantum one-counter one-way finite automaton. This result contrasts the case of one-way finite automata without counter, where it is known [5] that the quantum device is actually less powerful than its classical counterpart.

Multiple Usage of Random Bits in Finite Automata

2012

Finite automata with random bits written on a separate 2-way readable tape can recognize languages not recognizable by probabilistic finite automata. This shows that repeated reading of random bits by finite automata can have big advantages over one-time reading of random bits.

Local automata and completion

1993

The problem of completing a finite automata preserving its properties is here investigated in the case of deterministic local automata. We show a decision procedure and give an algorithm which complete a deterministic local automaton (if the completion exists) with another one, having the same number of states.

Ultrametric Finite Automata and Turing Machines

2013

We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the properties of probabilistic automata but complexity of probabilistic automata and complexity of ultrametric automata can differ very much.