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# Concurrent Test Generation

Vishwani D. Agrawal, vagrawal@eng.auburn.edu Alok S. Doshi, dosias@auburn.edu. Concurrent Test Generation. Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA For more details, see http://www.eng.auburn.edu/~vagrawal. Problem Statement.

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## Concurrent Test Generation

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1. Vishwani D. Agrawal, vagrawal@eng.auburn.edu Alok S. Doshi, dosias@auburn.edu Concurrent Test Generation Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA For more details, see http://www.eng.auburn.edu/~vagrawal Texas Instruments (India)

2. Problem Statement • To find the smallest test set to detect all single stuck-at faults in a combinational circuit. • An existing solution: • Group faults into fault sets using fault independence • Generate concurrent tests for each group • Contribution of this paper: Devise a simulation-based implementation for this solution. Texas Instruments (India)

3. Outline • Introduction • Simulation-based Independence Fault Collapsing • Simulation-based Concurrent Test Generation • Results • Conclusions Texas Instruments (India)

4. Introduction Problem of finding a minimal test: • Static compaction cannot guarantee optimality. • Dynamic compaction is complex. • Solution: Target both faults F1 and F2 at the same time to find a single test. We define this as concurrent test generation. . . . T(F2) T(F1) Test set for fault F2 Test set for fault F1 v2 v1 v3 Texas Instruments (India)

5. Fault Classification T(F1) T(F1) = T(F2) T(F2) F1 and F2 are equivalent. F1 dominates F2. T(F1) T(F2) T(F1) T(F2) F1 and F2 are independent. F1 and F2 are concurrently testable. Texas Instruments (India)

6. Definitions Independent Faults4: Two faults are independent if and only if they cannot be detected by the same test vector. Concurrently-Testable Faults: Two faults that neither have a dominance relationship nor are independent, are defined as concurrently-testable faults. 4 S. B. Akers, C. Joseph, and B. Krishnamurthy, “On the role of Independent Fault Sets in the Generation of Minimal Test Sets,” in Proc. International Test Conf., 1987, pp. 1100-1107. Texas Instruments (India)

7. Structural Independences sa1 sa1 sa1 sa0 sa1 sa0 sa1 sa1 sa1 sa0 sa0 sa0 sa1 sa1 sa0 sa0 sa0 sa0 sa1 sa0 Functional Independences: Found by ATPG-like methods. Texas Instruments (India)

8. Example Circuit 2 4 a x 1 5 b 3 7 11 c y d 6 10 9 All faults are Stuck-at-1 type e 8 C17 - ISCAS85 Benchmark Circuit 1 R. K. K. R. Sandireddy and V. D. Agrawal, “Diagnostic and Detection Fault Collapsing for Multiple Output Circuits,” Proc. Design, Automation and Test in Europe (DATE) Conf., Mar. 2005, pp. 1014 - 1019. Texas Instruments (India)

9. Independence Matrix and Graph Clique C17 - ISCAS85 Benchmark Circuit Texas Instruments (India)

10. Independence Fault Collapsing A “similarity” based algorithm [2] collapses the independence graph: Highly Similar Highly Dissimilar Similarity of a fault-pair 5,11,7 1,8 3,9,2 4,6,10 C17 - ISCAS85 Benchmark Circuit Equiv. Indep. 2 A. S. Doshi and V. D. Agrawal, “Independence Fault Collapsing,” Proc. 9th VLSI Design and Test Symp., Aug. 2005, pp. 357 - 364. Texas Instruments (India)

11. Simulation-based Independence Fault Collapsing • The independence graph generation procedure [2] requires ATPG. • Here we present a new method for graph generation using simulation: • Start with a fully-connected independence graph for an equivalence collapsed fault set. • Simulation of random vectors without fault dropping removes edges between faults detected by the same vector. 2 A. S. Doshi and V. D. Agrawal, “Independence Fault Collapsing,” Proc. 9th VLSI Design and Test Symp., Aug. 2005, pp. 357 - 364. Texas Instruments (India)

12. Simulation-based Independence Fault Collapsing 301 74181 4-bit ALU Texas Instruments (India)

13. Simulation-based Concurrent Test Generation • For each group, generate all test vectors for the first fault in the group. • If the number of test vectors for a fault is large, use a subset (e.g., 250 maximum) of vectors. • Simulate all faults in the group to select one vector that detects most faults in that group. • If more vectors than one detect the same number of faults within the group, then select the vector that detects most faults outside the group as well. Texas Instruments (India)

14. 74181 4-bit ALU Result Texas Instruments (India)

15. Results * Sun Ultra 5 *** Pentium Pro PC ** Hamzaoglu and Patel, IEEE-TCAD, 2000 Texas Instruments (India)

16. Number of Vectors for Increasing Circuit Sizes (100% Stuck-at Coverage) Single-fault ATPG (no compaction) Concurrent ATPG Minimum achieved! (dynamic compaction) Texas Instruments (India)

17. CPU Seconds for Increasing Circuit Sizes (100% Stuck-at Fault Coverage) Concurrent ATPG Minimum achieved! (dynamic compaction) Texas Instruments (India)

18. Conclusion • Concurrent test generation produces compact tests when combined with independence fault collapsing. • ATPG and set covering problems have exponential time complexities. Hence, we cannot expect absolute optimality for large circuits. • The concurrent ATPG procedure of this paper gives significantly smaller, and sometimes the optimum, test sets. • There is scope for improving the simulation-based algorithms for independence fault collapsing and concurrent test generation. Texas Instruments (India)

19. Thank You! Texas Instruments (India)

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