Fault Diagnosis and Fault Tolerance: A Systematic Approach by Tinghuai Chen

By Tinghuai Chen

With the swift progress of integration scale of VLSI chips and the current desire for trustworthy desktops in area exploration, fault analysis and fault toleran­ ce became extra vital than prior to, and therefore display loads of curiosity­ ing subject matters which magnetize many researchers to make numerous contribu­ tions to this box. lately, many new and critical effects were accomplished. a short experiment over the lawsuits of the meetings on fault­ tolerant computing and layout automation in addition to on checking out will persuade the reader of that. yet regrettably those achievements haven't been whole­ ly mirrored within the textbooks, in order that there appears to be like a spot for the recent researcher who already has the fundamental wisdom and desires to start examine during this sector. As a therapy for this deficiency, this ebook is meant for start­ ners, specifically graduate scholars, as a textbook with a purpose to make them the frontier of a few branches of the fault-tolerant computing box. the 1st bankruptcy introduces the four-valued good judgment B4 and its applica­ tions. In 1966 Roth first proposed this four-valued common sense as a method to generate checks for logical circuits, yet this paintings didn't hindrance the mathe­ matical foundation of B4 itself.

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Example text

In the first interpretation of the four-value logic. a is the normal and ~ is the faulty value: if for some input value. a and ~ at yare different and this internal difference can propagate to the output F. 56) is equivalent to the four-valued funtion (F,F) = D or D. If this four-valued function is denoted also by F. 56) to F* =1 or F* = 1. that is. 57) which means the internal difference (D or D) produced by the fault can be propagated (sensitized) to the output where it can be probed by. some equipment.

Then 3) 4) 5) I (x) = (\~ ). I~ = ~I = x. I(x-y) = (I~' Iv. I(x+y) = (I~ + I~). 41) I~ = ~I = x. I = (~\). krtl = (~I·~I). 44) + ~\). Xn) is a boolean function in B4 • then IE. = F( I~i' 1~2' .... ~ I. 46) where F is a boolean function in B2 . because 1~1 and ~I are variables in B2 . 2 is symmetric (commutative). 2 Multiplication table .. -.. x Ix o o x" -.. x o o o -.. x I~ o -.. 49) Fe,-"; 9) If holds, interchanging * ~ -.. 51) holds also. 2 Binary Coding Since front and rear values are added in B4 , it seems to be eight-valued logic.

13 is a two-level circuit; let us derive all the input values which cause hazards at the output. 1) The input-output function is and its component functions are FO = xOyi. Fi = Xi F =x + y. + yO + x*yO + xiy* + x*yo + Xi? + x*y* + x*? F* = X*yi + XO? + x*? F* = X*yi + xOy* + X*y*. 2) Identifying static hazards F eps From Feps Fig. 12 Example for identifying hazards (x + y)(y + y). only the terms xiy*. Xi? x*y*. X*? 18 1#. e. the F1h = Xl + yO + x*yO + x*yo. 17 consider e = X 0 Y1 . = xy + y; among the three terms of F* only the term x*y can cause the term xy of F e to produce D-D.

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