Additive Cellular Automata And Algebraic Series
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Additive Cellular Automata and Algebraic Series
Abstract: "A cellular automaton is an array of regularly interconnected identical cells. We study here the special case of automata where each cell depends in additive manner on its neighbours. The successives [sic] states of a given cell form a sequence whose generating series is proved to be always an algebraic series. We also examplify [sic] the realization of a given algebraic series by means of an automaton. As a byproduct we obtain a relation between additive cellular automata and certain 'automatic sequences' like the paper folding sequence."
Additive Cellular Automata
Author: Parimal Pal Chaudhuri
language: en
Publisher: John Wiley & Sons
Release Date: 1997-07-11
This book presents an extensive survey and report of related research on important developments in cellular automata (CA) theory. The authors introduce you to this theory in a comprehensive manner that will help you understand the basics of CA and be prepared for further research. They illustrate the matrix algebraic tools that characterize group CA and help develop its applications in the field of VLSI testing. The text examines schemes based on easily testable FSM, bit-error correcting code, byte error correcting code, and characterization of 2D cellular automata. In addition, it looks into CA-based universal pattern generation, data encryption, and synthesis of easily testable combinational logic. The book covers new characterizations of group CA behavior, CA-based tools for fault diagnosis, and a wide variety of applications to solve real-life problems.
Models of Massive Parallelism
Author: Max Garzon
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Locality is a fundamental restriction in nature. On the other hand, adaptive complex systems, life in particular, exhibit a sense of permanence and time lessness amidst relentless constant changes in surrounding environments that make the global properties of the physical world the most important problems in understanding their nature and structure. Thus, much of the differential and integral Calculus deals with the problem of passing from local information (as expressed, for example, by a differential equation, or the contour of a region) to global features of a system's behavior (an equation of growth, or an area). Fundamental laws in the exact sciences seek to express the observable global behavior of physical objects through equations about local interaction of their components, on the assumption that the continuum is the most accurate model of physical reality. Paradoxically, much of modern physics calls for a fundamen tal discrete component in our understanding of the physical world. Useful computational models must be eventually constructed in hardware, and as such can only be based on local interaction of simple processing elements.