제 4 주. Cellular Automata A Brief history of Cellular Automata P. Sarkar, ACM Computing Surveys, vol. 32, no. 1, pp. 80~107, 2000 학습목표 계산도구로서의 Cellular Automata 에 관한 역사적 연구주제 이해

개요 4 배경 –John von Neumann –Self-reproducing organisms  universal computation  modeling of natural phenomena – 참고 사이트 : 4 내용 –Classical : initial work of von Neumann –Modern: work of Wolfram –Games: Firing Squad problem

Classical (1) 4 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 4 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) 4 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 4 Fault-Tolerant Computing –Reliable Boolean circuit from unreliable components –Majority voting 4 Language and Pattern Recognition 4 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 4 Firing Squad Problem –Minsky, Game of Life –Conway, 1970 –Survival, birth, deaths 4 Sigma-Game –Sutner, 1990

Modern Research 4 Empirical Study –Wolfram : statistical parameters of the space-time patterns of CA evolution 4 Classification of CA 4 Limit Sets and Fractal Properties 4 Dynamics of CA 4 Computational Complexity 4 Finite CA and its Applications –VLSI applications

Homework #2 4 CA 를 진화방식으로 설계하는 방법을 제시하고, 간단한 프로그래밍으로 그 가능성을 보이라. 4 참고 : M. Mitchell, et al., “Evolving cellular automata to perform computations: mechanisms and impediments,” Physica D, vol. 75, no. 1-3, pp. 361~391, 마감일 : 4/1