By Igor L. Markov, John P. Hayes, Krishnaswamy

Good judgment circuits have gotten more and more at risk of probabilistic habit as a result of exterior radiation and technique version. additionally, inherently probabilistic quantum- and nano-technologies are at the horizon as we strategy the boundaries 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 basic, probabilistic reformulation of synthesis and trying out strategies. This monograph will current innovations for examining, designing, and checking out good judgment circuits with probabilistic habit.

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205. The overall error rate of the circuit is the sum of the error probabilities, weighted by S. 1007/978-90-481-9644-9_2, © Springer Science+Business Media Dordrecht 2013 21 22 2 Probabilistic Transfer Matrices the input combination probabilities. The probability of error for the circuit in Fig. 225. Note that joint probabilities of input combinations, rather than individual input probabilities, are necessary to capture correlations among inputs. We analyze circuit reliability and other aspects of non-deterministic behavior, using a representation called a probabilistic transfer matrix (PTM).

2 Consider the circuit C from Fig. 1, with inputs {w, x, y} and output {z}. The ITM is denoted J , and the PTM, shown in Fig. 2b, is denoted M. 1 at each gate, on all inputs. Fig. 6 shows intermediate matrices needed for this computation. The quantity fidelity(v, M, J ) is found by first element-wise multiplying J and M, then left-multiplying by an input vector v. 7432. 2560. The eliminate_variables operation is used to compute the “sub-PTM” of a smaller set of input and output variables. We formally define it for 1-variable elimination as follows.

Glitches of this type are propagated without attenuation. • Glitches of type 2 have amplitude A > Vt and duration 2T p > D > T p . Glitches of this type are propagated with an attenuated amplitude of A < A. • Glitches of type 3 have A < Vt . , they are electrically masked. Since amplitude is already indicated by the logic value, an additional bit is used to indicate whether the duration is larger or smaller than the propagation delay of the gate (when the amplitude is higher than the threshold voltage).