### Design, Analysis and Test of Logic Circuits Under Uncertainty (Lecture Notes in Electrical Engineering)

By Smita Krishnaswamy, Igor L. Markov

Common sense circuits have gotten more and more prone to probabilistic habit attributable to exterior radiation and method edition. furthermore, inherently probabilistic quantum- and nano-technologies are at the horizon as we technique the bounds of CMOS scaling. making sure the reliability of such circuits regardless of the probabilistic habit is a key problem in IC design---one that necessitates a primary, probabilistic reformulation of synthesis and checking out innovations. This monograph will current strategies for studying, designing, and trying out good judgment circuits with probabilistic habit.

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2 functions 000 001 010 011 a hundred one hundred and one a hundred and ten 111 (a) 1 1 1 zero zero 1 zero zero zero zero zero 1 1 zero 1 1 31 000 001 010 011 a hundred one zero one a hundred and ten 111 (b) 1 1 1 zero 1 1 1 zero zero zero zero 1 zero zero zero 1 000 001 010 011 a hundred a hundred and one one hundred ten 111 1 1 zero 1 1 zero zero zero zero zero 1 zero zero 1 1 1 (c) 000 001 010 011 a hundred a hundred and one a hundred and ten 111 zero. ninety five zero. ninety five zero. ninety five zero. 05 zero. 05 zero. ninety five zero. 05 zero. 05 (d) zero. 05 zero. 05 zero. 05 zero. ninety five zero. ninety five zero. 05 zero. ninety five zero. ninety five 000 001 010 011 a hundred one hundred and one a hundred and ten 111 1 zero zero 1 zero 1 1 zero zero 1 1 zero 1 zero zero 1 (e) Fig. 2. 10 PTMs for numerous forms of gate faults: a a fault-free excellent 2-1 MUX gate (select line is the third input); b first enter sign stuck-at 1; c first enter signs swapped; d probabilistic output bit-flip with p = zero.

60E-5 five. 38E-5 7. 06E-5 1. 58E-5 6. 96E-7 6. 63E-6 2. 62E-5 1. 31E-5 three. 00E-5 five. 39E-5 three. 87E-5 five. 37E-5 7. 69E-5 five. 34E-5 7. 24E-5 1. 38E-5 zero. 01 6. 05 zero. eighty three 2. eighty one four. 70 1. sixty seven 2. 38 1. 50 1. 24 zero. seventy five 2. fifty two 12. fifty four three. 06 6. 96E-7 6. 57E-6 2. 60E-5 1. 27E-5 2. 97E-5 five. 35E-5 three. 93E-5 five. forty-one E-5 7. 71E-5 five. 35E-5 7. 23E-5 1. 63E-5 zero. 01 four. 87 zero. eighty three zero. seventy eight three. five zero. ninety four three. ninety seven 2. 20 1. forty five zero. fifty six 2. forty-one three. sixteen 2. sixty five five. four Empirical Validation We now record empirical effects for SER research utilizing AnSER and our SERaware synthesis suggestions. The experiments have been performed on a 2.

1 2 2 four five 7 7 eight eleven 15 sixteen 17 2 Probabilistic move Matrices . . . . . . 2. 1 PTM Algebra . . . . . . . . . . . . . . . . 2. 1. 1 easy Operations . . . . . . . . . 2. 1. 2 extra Operation . . . . . . 2. 1. three dealing with Correlations . . . . . 2. 2 functions . . . . . . . . . . . . . . . . . 2. 2. 1 Fault Modeling . . . . . . . . . . 2. 2. 2 Modeling Glitch Attenuation 2. 2. three errors move services . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ninety three ninety three ninety four ninety six ninety seven ninety eight ninety nine a hundred 103 104 104 106 107 113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents . . . . . . . one hundred fifteen one hundred fifteen 116 116 117 119 one hundred twenty Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7 precis and Extensions . . . . . . . . . . . . . . . . . 7. 1 precis . . . . . . . . . . . . . . . . . . . . . . . . . 7. 2 destiny instructions. . . . . . . . . . . . . . . . . . . . 7. 2. 1 approach diversifications and getting older results 7. 2. 2 research of organic structures. . . . . 7. three Concluding comments . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

Inn−1 and PTM M, allow ink and inl be inputs which are pointed out with (connected to) one another. Then eliminate_r edundant_variables(M, ink , inl ) = M , the place M is a matrix with n − 1 enter variables whose rows are 2. 1 PTM Algebra 29 a b e F2 G1 (a) 000 001 010 011 a hundred a hundred and one a hundred and ten 111 1 zero 1 zero 1 zero zero zero zero 1 zero 1 zero 1 zero zero zero zero zero zero zero zero 1 zero (b) zero zero zero zero zero zero zero 1 00 01 10 eleven 1 zero 1 zero zero 1 zero zero zero zero zero zero zero zero zero 1 (c) Fig. 2. eight sign forwarding utilizing eliminate_r edundant_variables: a circuit with sign b fanning out to 2 diverse degrees; b AND ⊗ I , including b as an enter and output; c ultimate ITM for circuit computed via removal rows in boldface M (i 1 .