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Multi-Wires Removal and Rectification using Interpolants: A Methodology Overview

This document details a method for the simultaneous removal of multiple wires in a circuit while ensuring the rectification of its functionality. The method employs a two-way RAR (Redundant Addition Removal) technique, utilizing Boolean manipulation to activate faults and propagate corrections effectively. It introduces the concept of interpolants for refining networks, providing examples and outlines for constructing rectified networks. This comprehensive overview is aimed at enhancing circuit designs by addressing fault management through innovative approaches.

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Multi-Wires Removal and Rectification using Interpolants: A Methodology Overview

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  1. Multi-wires Removal and Rectification Using Interpolant Speaker: Guo-JhuHunag Advisor: Chun-Yao Wang 2009/11/20

  2. Outline • Problem Formulation • How Interpolant Construct Rectified Network for Single Wire

  3. Problem Formulation • Given a circuit, we want to remove many wires simultaneously and rectify the functionality.

  4. MA to Boolean manipulation wt wt s-a-1 fault The fault activation –fwt(X) is the set of minterms to cause the different value at f between good circuit and bad circuit The fault propagation –ODCwt(X) is the set of minterms to propagate the different value to PO

  5. MA to Boolean manipulation wt wt s-a-1 fault MA(wt) = –fwt(X)  –ODCwt(X)

  6. Rectified Network Using Two-way RAR method • Two-way(one-stage) RAR method • MA(wt) -> <g,v> • MA(gd) -> <g,-v>

  7. wt gt gd gs MA(wt)= -fgt(X)-ODCgt(X) MA(gd)= fgd(X)-ODCgd(X) = fgt(X)-ODCgt(X)

  8. Rectified Network Using Interpolant • Interpolant • MA(wt) -> <g,0> • MA(gd) -> <g,1> • -fgt(X)-ODCgt(X)  -g(X) • fgt(X)-ODCgt(X)  g(X) wt gt gd gs 

  9. Example wt a g1 gd b c g4 a g3 d -g1(X)  -ODCg1(X) = { a’b’cx, a’b’cd’} g1(X)  -ODCg1(X) = { axcd’, a’bcx, xbcd’ } -g1(X) = -(a+b) ={ a’b’xx } g1(X) = (a+b) = { axxx, xbxx } -ODCg1(X) = { a’xcx, xxcd’ }

  10. Example -g1(X)  -ODCg1(X) = { a’b’cx, a’b’cd’} -g(X) g1(X)  -ODCg1(X) = { axcd’, a’xcx, bxcd’ }  g(X) K-map of g(X)

  11. Example a b a g1 gd b c g4 a g3 d a+b

  12. IRRA Example a b a g1 gd b c g4 a g3 d

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