S. Ercolani et al., "Estimate of Signal Probability in Combinational Logic Networks," IEEE European Test Conference, pp. 132-138, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....M M Delay Figure 2. Decoupling of delays. Since P (x) Pfx(t) 1g (by theorem 1) and M has zero delay, then the problem of propagating equilibrium probabilities through it is identical to that of propagating signal probabilities through logic circuits, which has been well studied [5] [9]. Since the internal structure of M is not known, the problem is actually even more generic than that, and can be expressed as given a Boolean function f(x 1 ; x n ) and that each x i can be high with probability P (x i ) what is the probability that f is high Any number of ....

....fanout and feedback will cause internal nodes to be correlated, and destroy the independence property. This problem is central to any circuit analysis based on a statistical representation of signals, and can usually be taken care of by using heuristics that trade off accuracy for speed [5 9]. Based on our previous experience with the propagation of probability waveforms [12] we have found that, if the modules are large enough so that tightly coupled nodes (such as in latches or small cells) are kept inside the same module, then the coupling outside the modules is sufficiently low ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricc'o, "Estimate of signal probability in combinational logic networks," 1989.

....building an OBDD corresponding to the global function of the node (i.e. function of the node in terms of the circuit inputs) and then performing a postorder traversal of the OBDD using equation: 3) This leads to a very efficient computational procedure for signal probability estimation. In [21], a procedure for propagating signal probabilities from the circuit inputs toward the circuit outputs using only pairwise correlations between circuit lines and ignoring higher order correlation terms is described. In [61] and [40] the temporal correlation between values of some signal x in two ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. "Estimate of signal probability in combinational logic networks. " In First European Test Conference, pages 132--138, 1989.

....During calculation of the signal transition probabilities at node outputs, the mutual correlation between primary inputs can be accounted for by considering conditional probabilities between all subsets of inputs. An efficient approximation of this is the use of pairwise conditional probabilities [10]. The temporal correlation at the primary inputs, i.e. correlation between the values at each input across clock cycles, can be dealt with by directly using transition probabilities at primary inputs for calculating the transition probabilities at node outputs. Given the above assumptions, ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivio, and B. Ricco. Estimate of signal probability in combinational logic networks. In Proceedings of the European Test Conference, pages 132--138, April 1989.

....M M Delay Figure 2. Decoupling of delays. Since P (x) Pfx(t) 1g (by theorem 1) and M 0 has zero delay, then the problem of propagating equilibrium probabilities through it is identical to that of propagating signal probabilities through logic circuits, which has been well studied [5] [9]. Since the internal structure of M 0 is not known, the problem is actually even more generic than that, and can be expressed as given a Boolean function f(x 1 ; x n ) and that each x i can be high with probability P (x i ) what is the probability that f is high Any number of ....

....fanout and feedback will cause internal nodes to be correlated, and destroy the independence property. This problem is central to any circuit analysis based on a statistical representation of signals, and can usually be taken care of by using heuristics that trade off accuracy for speed [5 9]. Based on our previous experience with the propagation of probability waveforms [12] we have found that, if the modules are large enough so that tightly coupled nodes (such as in latches or small cells) are kept inside the same module, then the coupling outside the modules is sufficiently low to ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricc'o, "Estimate of signal probability in combinational logic networks," 1989 IEEE European Test Conference, pp. 132--138, 1989.

....equilibrium probabilities and transition densities from its inputs to its outputs. Since M 0 has zero delay, then the problem of propagating equilibrium probabilities through it is identical to that of propagating signal probabilities through logic circuits, which has been well studied [4] [8]. Since the internal structure of M 0 is not known, the problem is actually even more generic than that, and can be expressed as given a Boolean function f(x 1 ; x n ) and that each x i can be high with probability P (x i ) what is the probability that f is high Any number of ....

....fanout and feedback will cause internal nodes to be correlated, and destroy the independence property. This problem is central to any circuit analysis based on a statistical representation of signals, and can usually be taken care of by using heuristics that trade off accuracy for speed [4 8]. Based on our experience with the propagation of probability waveforms [11] we have found that, if the modules are large enough so that tightly coupled nodes (such as in latches or small cells) are kept inside the same module, then the coupling outside the modules is sufficiently low to justify ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricc'o, "Estimate of signal probability in combinational logic networks," 1989 IEEE European Test Conference, pp. 132--138, 1989.

....(42) m S 1 S 2 S 1 is an inferior solution for n, but may lead to optimal solution for m. n i 1 n i 1 m m S 1 S 2 w 1 w 2 (a) b) i 1 Figure 9: An example to illustrate complications due to a real delay model. that is, C(i; j) P (ijj) P (i) P (jji) P (j) 43) Ercolani et al. [8] describe a method to approximate the correlation coefficients of the outputs of gates given the signal probabilities and correlation coefficients of the inputs as follows. Let g be a gate with inputs i and j and the correlation coefficients of i and j, i and m, and j and m be given as C(i; j) ....

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. Estimate of signal probability in combinational logic networks. In Proceedings of the European Test Conference, pages 132--138, 1989.

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S. Ercolani et al., "Estimate of Signal Probability in Combinational Logic Networks," IEEE European Test Conference, pp. 132-138, 1989.

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S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. Estimate of signal probability in combinational logic networks. In First European Test Conf., pages 132--138, 1989. 34

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S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. Estimate of signal probability in combinational logic networks. In First European Test Conf., pages 132--138, 1989.

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S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. Estimate of signal probability in combinational logic networks. In Proceedings of the European Test Conference, pages 132--138, 1989.

No context found.

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. Estimate of signal probability in combinational logic networks. In First European Test Conf., pages 132--138, 1989.

No context found.

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. " Estimate of signal probability in combinational logic networks. " In First European Test Conference, pages 132--138, 1989.

No context found.

S. Ercolani, M. Favalli, M. Damiani, P. Olivo, and B. Ricco. " Estimate of signal probability in combinational logic networks. " In First European Test Conference, pages 132--138, 1989.

No context found.

S. Ercolani, M. Favalli, M. Mamiani, P. Olivo, and B. Ricco, "Estimate of signal probability in combinational logic networks," in Proceeding of IEEE European Test Conference, pp. 132--138, 1989.

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