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# Improvement to Probabilistic Static Analysis

IP.com Disclosure Number: IPCOM000111146D
Original Publication Date: 1994-Feb-01
Included in the Prior Art Database: 2005-Mar-26
Document File: 4 page(s) / 84K

IBM

Savir, J: AUTHOR

## Abstract

Probabilistic Static Analysis (PSAS) can be improved by the use of a probability calculator to compute signal probabilities of the tree portions of the combinational networks, and the expansion operations to eliminate fanouts. This combination of methods will allow a fast computation of signal probabilities since the proposed calculation for tree portions of the circuit has a linear computational complexity. It is expected that the following improvement will decrease the running time dramatically.

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Improvement to Probabilistic Static Analysis

Probabilistic Static Analysis (PSAS) can be improved by the use
of a probability calculator to compute signal probabilities of the
tree portions of the combinational networks, and the expansion
operations to eliminate fanouts.  This combination of methods will
allow a fast computation of signal probabilities since the proposed
calculation for tree portions of the circuit has a linear
computational complexity.  It is expected that the following
improvement will decrease the running time dramatically.

PSAS is an implementation of Shannon's Boolean expansion, used
to compute detection probabilities of faults (usually of stuck-at
type) in a combinational circuit.  The heart of the method is the
computation of the probability that a line will carry the signal
value "1", called the signal probability.

The probability calculation for trees is shown in Fig. 1.  The
formulas for NAND and NOR can be computed from the figure by noting
that NAND stands for an AND-NOT, and NOR for an OR-NOT.

The combined approach is described in the following procedure:

Procedure 1:

Step 1: Compute signal probabilities using tree formulas up to the
first fanout boundary.

Step 2: Switch to PSAS.  Advisable to expand along fanout points.
Each time a subnet is a tree, switch to the probability calculator to
compute the result.

The following example shows how the algorithm works.

Example 1:

Consider the circuit of Fig. 2a.  We would like to compute the signal
probability of the line F. Fig. 2a also shows the signal
probabilities, computed by the formulas of Fig. 1, for the lines up
to the fanout poin...