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Unformatted text preview: Click to edit Master subtitle style 8/1/11 Cellular Automata Anthony Lora 8/1/11 What are Automata? Von Neumans Machine A Simple CA CA ?= TM Features Examples Outline 8/1/11 A selfoperating machine or mechanism Automata Theory: Study of abstract, mathematical machines and systems. Includes: Deterministic Finite Automata (DFA) Nondeterministic Finite Automata (NFA) Pushdown Automata (PDA) Turing Machines (TM) Cellular Automata (CA) What is an Automaton? 8/1/11 Proposed by John von Neumann in the late 1940s to model selfreproducing organisms If a machine were surrounded by hardware soup, could it create a working copy of itself? Possible if the machine had a blueprint for itself Make a copy of the blueprint and use it as instructions for building Stanislaw Ulam suggested using cells to represent the parts Cellular Automata 8/1/11 Onedimensional array of cells Each cell has a state Time is divided into discrete units A function (the local rule) determines how cell state changes State change determined by the cells state and the state of its two neighbors At each clock tick, the local rule is run on the cells in parallel A Simple CA 8/1/11 Possible states: 0, 1 Rules: If 1, become 0 If 0 and neighbors are 0, then remain 0 If 0 and at least one neighbor is 1, then become 1 Example { F E 8 5 6 E 9 C 8 D B 9 4 A 9 A 0 1 7 3 F 4 0 6 2 A 0 D 1 8 } T = 0 { C E B 9 3 C 6 B 2 8 2 4 D 5 A C 6 2 7 6 B 5 0 A B C 5 8 3 } { E 3 0 A 2 1 9 3 7 1 9 4 4 9 8 4 A 9 B 9 5 8 1 2 A 7 9 B D 4 3 } T = 1 1 { 0 F 9 7 D E B 0 1 A 4 C 0 7 A 2 6 7 8 C B E C 9 1 3 5 8 0 } T = 2 1 { 3 9 4 C 4 2 B 3 C A E 5 4 0 1 D A 6 C 6 4 E 0 F 2 0 6 5 B 9 B 0 } 1 { 9 8 C D 2 8 B 8 F 5 7 4 C 5 F 9 B E 3 3 E 1 3 2 C 8 D C 4 5 } { 8 5 8 2 A 3 1 D 3 F 0 8 4 F E B 9 3 9 C 4 7 B 5 B 5 3 6 F 6 4 } 1 { 8 5 C 9 3 4 8 E 2 9 D 4 D 6 9 A C 5 2 D F 8 3 F F 5 9 7 F E } 1 { 4 1 E F D C 2 7 3 1 5 4 4 1 B 3 A 8 A 8 5 B D 3 1 0 D 4 E B 7 } { F E 8 5 6 E 9 C 8 D B 9 4 A 9 A 0 1 7 3 F 4 0 6 2 A 0 D 1 8 } T = 3...
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 Spring '11
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 Computer Science

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