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Published on August 9, 2007

Author: Pumbaa

Source: authorstream.com

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Threshold for Life:  Threshold for Life MIT Media Laboratory Prof. Isaac Chuang Objective:  Objective Claim: Life can be constructed from faulty components An Amazing Theorem:  An Amazing Theorem von Neumann (1956) Quantum version: Preskill, Shor, Aharonov, Ben-Or, Gottesman, Chuang*,… * D. Gottesman and I. Chuang, Nature, vol. 402, p. 390, 1999 Fault-Tolerant Circuits:  Fault-Tolerant Circuits Fault-Tolerant Circuits:  Fault-Tolerant Circuits The Fault-Tolerance Threshold:  The Fault-Tolerance Threshold A circuit containing N (error-free) gates can be simulated with probability of error andlt; e, using cdN faulty gates, which fail with probability p, if pandlt;pth. Proof: Assume 3-input gates. N=1 easy. Efficient Fault Tolerance:  Efficient Fault Tolerance A circuit containing N (error-free) gates can be simulated with prob. of error andlt; e, using O(N log N) faulty gates, which fail with prob. p, if pandlt;pth. Status: pth ¼ 1/6 (Hajek andamp; Weller ’91) Fault-Tolerant Life:  Fault-Tolerant Life Nature does not seem to use such constructions How can life be made fault-tolerant? What is Life?:  What is Life? Desirable characteristics: Self repair Self reproduction Growth Evolution Schrodinger von Neumann (1966) Theory of Self-Reproducing Automata: elementary machine capable of reproduction and universal computation Von Neumann’s Automaton:  Von Neumann’s Automaton Model based on 29 state Cellular Automaton (simulation from H-H Chou) Langton’s 8-state replicator (not universal) Universal Turing machine Universal constructor Visions of Fault-Tolerant Life:  Visions of Fault-Tolerant Life Two interesting questions: What is the fault-tolerance threshold for Life? Rad-hard biology Immortal Biosystems …Reproduction?

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