제 4 주 . Cellular AutomataA Brief history of Cellular Automata

P. Sarkar, ACM Computing Surveys, vol. 32, no. 1, pp. 80~107, 2000

학습목표계산도구로서의 Cellular Automata 에 관한 역사적 연구주제

이해

개요 배경

– John von Neumann

– Self-reproducing organisms universal computation modeling of natural phenomena

– 참고 사이트 : http://alife.santafe.edu/alife/topics/cas/ca-faq

내용– Classical : initial work of von Neumann

– Modern: work of Wolfram

– Games: Firing Squad problem

Classical (1)

Beginnings

– 1D array, discrete, local rule (change state based on present state and left/right neighbors)

– Formal model of self-reproducing biological systems

– Axiomatic / deductive treatment to the study of “complicated” natural systems

– Self-reproducing automata : sum of left neighbor and itself modulo k

– Computation universality : step by step simulation of TM Variants of Cellular Automata

– Cell states : polygeneous CA

– Geometry : static CA, node static CA, dynamic CA

– Neighborhood : totalistic CA

– Local rule : programmable CA

– Tesselation automata : time-varying CA

– Iterative automata, one-way CA

Classical (2)

Biological Connection

– L-systems : model of growth for filamentary organisms based on ideas of CA

– Self-reproduction and artificial life : computation universality is not a fundamental requirement for a self-reproducing automata spontaneous emergence of self-replicating systems

Fault-Tolerant Computing

– Reliable Boolean circuit from unreliable components

– Majority voting Language and Pattern Recognition Invertibility, Surjectivity and Garden of Eden

– CA is invertible iff its global map is injective

– Global map is surjective iff its restriction to finite configuration is injective

– Garden of Eden : not reachable configuration

CA Games

Firing Squad Problem

– Minsky, 1957 Game of Life

– Conway, 1970

– Survival, birth, deaths Sigma-Game

– Sutner, 1990

Modern Research

Empirical Study

– Wolfram : statistical parameters of the space-time patterns of CA evolution

Classification of CA Limit Sets and Fractal Properties Dynamics of CA Computational Complexity Finite CA and its Applications

– VLSI applications

Homework #2

CA 를 진화방식으로 설계하는 방법을 제시하고 , 간단한 프로그래밍으로 그 가능성을 보이라 .

참고 : M. Mitchell, et al., “Evolving cellular automata to perform computations: mechanisms and impediments,” Physica D, vol. 75, no. 1-3, pp. 361~391, 1994.

마감일 : 4/1