On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach

VLSI Design, Sep 2018

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.

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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)


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M. Srinivas, L. M. Patnaik. On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach, VLSI Design, 4, DOI: 10.1155/1996/75798