Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Barua, Rana (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to existing problems are being constantly Bought and discovered.An important boost to the atudy of cellular autamata was provided by Wolfram, in his experimental and theoretical studies conducted in the mid-eighties. It is in this period that finite cellular automata began to be studied seriously. The paper by Martin, Odlyzko and Wolfram in 1986 (115), is the first attempt to study a special class of finite cellular automata "called additive (or linear) cellular automata By using algebraic techniques, they were able to derive a large number of results on the state transition diagram (STD) of this elass of cellular automata. In the process it became evident that algebraic techniques were going to play a pivotal role in the further exploration of linear cellular automata. The next important step in the study of finite linear cellular automata is its application to designing VLSI structures. It has been argued that the régular and homogeneous nature of cellular sutomata are well suited foe VLSI implementation and has spurred a grest body of research in suggesting alternative cellular automata based structures for many practăcal applications. This work has almost exclusively concentrated on linear (or affine) cellular automata, since this kind can be tacklod using linear algebra. On the other hand non- linear cellular automata are not amenable to known mathematical techniques and bence little work bas been done towards finding VLSI application of this kind of cellular automata. However, the diversity of non-linear oellular automata holds out great promise. The work on application oriented aspects of finite linear celiular automata have led to some interesting results. On the other band, finite linear cellular automata were also being studied from amore theoretical viewpoint and led to interesting algebraie techniques. The important object from both theoretical and practical viewpoints is the structure of the state transition diagram (STD). While VLSI applications concentrate on designing hybrid cellular automata whose STD have certain desirable properties, theoretical investigations fix a cellular automata and try to analyse the STD completely.In this thesis, we take a more theoretical approach, though a VLSI implementable cellular automata based private key cryptosystem is proposed in Chapter 7. An impartant theme of the whole thesis is the study of the reversibility of different kinds of finite linear cellular automata. A major contribution of the thesis is to provide and in some cases develop algebraic foundation for the study of the above class of cellular sutomata on ane or more dimensions.1.1 Thesis plan In the rest of the thesis we will abbrevinte both cellular automata and celular satomaton by CA.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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