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On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach
VLSI DESIGN
On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach
M. SRINIVAS 0
L. M. PATNAIK 0
0 aMotorola India Electronics Limited , 33A, VLSoor Road, Bangalore 560042 , INDIA; bMicroprocessor Applications Laboratoo; Indian Institute of Science , Bangalore 560 012 , INDIA
Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed. A brief overview of Genetic Algorithms (GAs) and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance of our GAbased approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger. To account for the relatively quick convergence of the gradient descent methods, we analyze the landscape of the COP-based cost function. We prove that the cost function is unimodal in the search space. This feature makes the cost function amenable to optimization by gradient-descent techniques as compared to random search methods such as Genetic Algorithms.
Testing; Random Test Vectors; Signal Probabilities; Genetic Algorithms; COP testability measure
1. INTRODUCTION
Test techniques for detecting faults in combinational
digital circuits may be broadly classified into two
catdomly generated vectors are determined from
relatively more macroscopic features of the circuit.
Fault simulation is a key component of random test
methods. A fault simulator is used to simulate the
beegories--deterministic methods and random methods.
haviour of the circuits with and without the presence
Deterministic methods make use of algorithms that
of faults. Based on the output responses of the
faultexploit detailed circuit information to generate the test
free circuit and the circuit with the faults, the
ranvectors, while random test methods employ randomly
domly generated vector is classified as a test vector.
generated vectors and fault simulation to locate test
vectors. The distributions of the 0s and Is in the
ranA decade ago, random test methods were
inefficient in comparison to deterministic methods,
primarily due to two reasons (i) high costs of fault
simulation and (ii) prohibitively long test sequences for
?resistant? circuits. Recent advances have mitigated
the effects of both factors. The costs of fault
simulation have been steadily decreasing until date. Also the
use of non-uniform distributions and multiple
distributions for generating the random vectors has
considerably decreased the number of vectors to be
simulated for attaining maximal fault coverage.
Research on improving the performance of random
test methods dates back to the seventies
[
2
][ ][
16
][
19
]. Agrawal et.al. [
4
] have demonstrated
that the number of vectors to be simulated to detect
all detectable faults in a circuit can be significantly
reduced by using inequiprobable 0s and Is in the test
vectors. Schurmann et al. 19] use adaptively varying
input distributions (signal probabilities) to reduce the
length of test sequences. Wunderlich [
22
] and
Lisanke [
14
] have formulated the problem as one of
optimizing a ?cost? associated with the set of signal
probabilities. In both cases, gradient descent-based
optimization techniques have been utilized. More
recently Wunderlich [
24
] has discussed the advantages
of employing multiple distributions for generating the
test vectors; both theoretical and experimental
evidence point to the utility of the approach. Other
related work includes [
12
][
13
][
15
][
17
][
23
].
In this paper we consider the problem of
optimizing input distributions (of 0s and Is) for generating
random test vectors. We demonstrate the application
of Genetic Algorithms (GAs), powerful search and
optimization techniques, to determine the optimal
input signal probabilities. Genetic Algorithms have
evolved as robust optimization and search procedures
for a wide range of complex problems. In several
cases, GAs have located solutions better than
traditional problem-specific algorithms. The task of
optimizing the input signal probabilities for generating
random vectors is a complex one, primarily due to
the complexity of the circuits and the non-trivial
interactions among the input signals.
Essential to every optimization problem is a cost
that may be associated with each solution that reflects
the quality of the solution. The cost function
that we employ to evaluate the signal probabilities is
based on the COP testability measure [
5
], and
formulated by Lisanke et al. 14]. The efficacy of the GA in
optimizing the input signal prob (...truncated)