Noise Threshold for Universality of Two-Input Gates

It is known that epsi-noisy gates with two inputs are universal for arbitrary computation (i.e., can compute any function with bounded error), if all gates fail independently with probability epsi and epsi < beta 2 = (3 - radic7)/4 ap 8.856%. In this paper, it is shown that this bound is tight fo...

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Veröffentlicht in:	IEEE transactions on information theory 2008-08, Vol.54 (8), p.3693-3698
1. Verfasser:	Unger, F.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Approximation Circuit faults Circuit noise Circuits Computation with unreliable components Computational modeling Computer errors Electric noise Electronics Errors Exact sciences and technology fault-tolerant computation Gates Information theory Information, signal and communications theory Mathematical analysis Mathematical models Noise Noise robustness Noise threshold Telecommunications and information theory Thresholds Upper bound
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Zusammenfassung:	It is known that epsi-noisy gates with two inputs are universal for arbitrary computation (i.e., can compute any function with bounded error), if all gates fail independently with probability epsi and epsi < beta 2 = (3 - radic7)/4 ap 8.856%. In this paper, it is shown that this bound is tight for formulas, by proving that gates with two inputs, in which each gate fails with probability at least beta 2 cannot be universal. Hence, there is a threshold on the tolerable noise for formulas with two-input gates and it is beta 2 . It is conjectured that the same threshold also holds for circuits.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2008.926459