Formal Logic of Cellular Automata (original) (raw)

CELLULAR AUTOMATA : A SURVEY OF IT'S WIDESPREAD APPLICATION

A cellular automaton is a discrete model studied in computability theory , mathematics, physics and myriad of other areas. It's profound application makes it indispensable in the scientific community. This paper is intended to provide an overview of the concept of cellular automata and it's application in different areas. In this report I have highlighted some general application of cellular automata with the later section of the paper emphasizing more on the application of cellular automata in the field of parallel computing.

Some applications of propositional logic to cellular automata

Mathematical Logic Quarterly, 2009

In this paper we give a new proof of Richardson's theorem [31]: a global function G A of a cellular automaton A is injective if and only if the inverse of G A is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular automata formulated by Durand [12].

One dimensional cellular automata-The totalistic approach

2018

The topic of cellular automata has many interesting and wide ranging applications to real life problems emerging from areas such as image processing, cryptography, neural networks, developing electronic devices and modelling biological systems. In fact cellular automata can be a powerful tool for modelling many kinds of systems. In the March 2018 issue of At Right Angles we had introduced the basic ideas which form the foundation of the Elementary Cellular Automata (ECA) as defined by Stephen Wolfram. The reader is urged to go through the article before reading this. The topic of Cellular Automata lends itself to interesting investigations which are well within the reach of high school students. We had illustrated the simple and yet powerful ideas in the previous article where we had described and analysed the behaviour of the 256 ECAs. In this article we shall provide a brief recap for the first time reader before moving on to the concept of Totalistic Cellular Automata

Lattice-driven cellular automata implementing local semantics

Physica D: Nonlinear Phenomena, 2008

We propose a model based on Elementary Cellular Automata (ECA) where each cell has its own semantics defined by a lattice. Semantics play the following two roles: (1) a state space for computation and (2) a mediator generating and negotiating the discrepancy between the rule and the state. We call semantics playing such roles 'local semantics'. A lattice is a mathematical structure with certain limits. Weakening the limits reveals local semantics. Firstly, we implement local semantics for ECA and call the result 'Lattice-Driven Cellular Automata' (LDCA). In ECA rules are common and invariant for all cells, and uniquely determine the state changes, whereas in LDCA rules and states interplay with each other dynamically and directly in each cell. Secondly, we compare the space-time patterns of LDCA with those of ECA with respect to the relationship between the mean value and variance of the 'input-entropy'. The comparison reveals that LDCA generate complex patterns more universally than ECA. Lastly, we discuss the observation that the direct interplay between levels yields wholeness dynamically.

Linear cellular automata and finite automata

Cellular Automata: A Parallel Model, Kluwer, http://www …, 1999

Moreover, automata theory motivates many algorithms that are of use in the study of cellular automata. Below we will present a simple algorithm that tests whether a cellular automata is reversible, m-to-1 or surjective. For reversible cellular automata, the algorithm also ...

Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour

2019

Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular automaton with a 2-linear time and display its spatial dynamics. Three particular Turing machines are converted in three universal one-dimensional cellular automata, they are: binary sum, rule 110 and a universal reversible Turing machine.

A survey on cellular automata

2003

A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. Researchers, scientists and practitioners from different fields have exploited the CA paradigm of local information, decentralized control and universal computation for modeling different applications. This article provides a survey of available literature of some of the methodologies employed by researchers to utilize cellular automata for modeling purposes. The survey introduces the different types of cellular automata being used for modeling and the analytical methods used to predict its global behavior from its local configurations. It further gives a detailed sketch of the efforts undertaken to configure the local settings of CA from a given global situation; the problem which has been traditionally termed as the inverse problem. Finally, it presents the different fields in which CA have been applied. The extensive bibliography provided with the article will be of help to the new entrant as well as researchers working in this field.

Expressiveness of Elementary Cellular Automata

International Journal of Modern Physics C, 2013

We investigate a expressiveness, a parameter of one-dimensional cellular automata, in the context of simulated biological systems. The development of elementary cellular automata is interpreted in terms of biological systems, and biologically inspired parameters for biodiversity are applied to the configurations of cellular automata.

A study of fuzzy and many-valued logics in cellular automata

Computing Research Repository, 2006

In this paper we provide an analytical study of the theory of multi-valued and fuzzy cellular automata where the fuzziness appears as the result of the application of an underlying multi-valued or continuous logic as opposed to standard logic as used conventionally. Using the disjunctive normal form of any one of the 255 ECA's so defined, we modify the underlying logic structure and redefine the ECA within the framework of this new logic. The idea here is to show that the evolution of space-time diagrams of ECA's under even a probabilistic logic can exhibit non-chaotic behavior. This is looked at specifically for Probabilistic Rule 110, in contrast with Boolean Rule 110 which is known to be capable of universal computation.