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Independence Fault Collapsing

Alok S. Doshi (Speaker) Vishwani D. Agrawal. Independence Fault Collapsing. Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA. Outline. Motivation Fault Classification Independence Graph and Matrix Independence Fault Collapsing

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Independence Fault Collapsing

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  1. Alok S. Doshi (Speaker) Vishwani D. Agrawal Independence Fault Collapsing Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA VDAT05: Doshi and Agrawal

  2. Outline • Motivation • Fault Classification • Independence Graph and Matrix • Independence Fault Collapsing • Concurrent Test Generation • Conclusions and Future Work VDAT05: Doshi and Agrawal

  3. Motivation a x b c y d e C17 - ISCAS85 Benchmark Circuit 1T. M. Niermann and J. H. Patel, “HITEC: A Test Generation Package for Sequential Circuits,” Proc. European Design Automation Conference, Feb. 1991, pp. 214-218. 2 T. P. Kelsey, K. K. Saluja, and S. Y. Lee, “An Efficient Algorithm for Sequential Circuit Test Generation,” IEEE Trans. Computers, vol. 42, no. 11, pp. 1361-1371, Nov. 1993. 3 W. T. Cheng and T. J. Chakraborty, “Gentest: An Automatic Test Generation System for Sequential Circuits,” Computer, vol. 22, no. 4, pp. 43–49, April 1989. VDAT05: Doshi and Agrawal

  4. Fault Classification VDAT05: Doshi and Agrawal

  5. 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. VDAT05: Doshi and Agrawal

  6. Structural Independences sa1 sa1 sa1 sa0 sa1 sa0 sa1 sa1 sa1 sa0 sa0 sa0 sa1 sa1 sa0 sa0 sa0 sa0 sa1 sa0 VDAT05: Doshi and Agrawal

  7. Implied Independences Equivalence implied independence: If two faults are equivalent then all faults that are independent of one fault are also independent of the other fault. Dominance implied independence: If one fault dominates a second fault then all faults that are independent of the first fault are also independent of the second fault. VDAT05: Doshi and Agrawal

  8. Functional Independences VDAT05: Doshi and Agrawal

  9. Example Circuit 2-1 4-1 a x 5-1 1-1 b 3-1 7-1 c 11-1 y d 6-1 10-1 9-1 e 8-1 C17 - ISCAS85 Benchmark Circuit 5 R. K. K. R. Sandireddy and V. D. Agrawal, “Diagnostic and Detection Fault Collapsing for Multiple Output Circuits," in Proc. Design, Automation and Test in Europe (DATE) Conf., Mar. 2005, pp. 1014 - 1019. VDAT05: Doshi and Agrawal

  10. Independence Matrix and Graph VDAT05: Doshi and Agrawal

  11. Clique A clique is defined as a fully-connected subgraph, i.e., a subgraph in which every node is connected to every other node. A lower bound on the number of tests required to cover all faults of an irredundant combinational circuit is given by the size of the largest clique of the independence graph. VDAT05: Doshi and Agrawal

  12. Cliques VDAT05: Doshi and Agrawal

  13. Degree of Independence Degree of Independence: This is the number of edges attached to the fault node and is computed for the ith fault by adding all the elements of either the ith row or the ith column of the independence matrix. DI (ith fault) = Σ xij = Σ xji N N j=1 i=1 VDAT05: Doshi and Agrawal

  14. Degree of Independence VDAT05: Doshi and Agrawal

  15. Similarity Metric Similarity Metric: This is a measure defined for a pair of faults that determines how similar they are in their independence and concurrent-testability with respect to the entire fault set of the circuit. SIM (fault-i, fault-j) = Nxij + (1-xij) Σ |xik-xjk| N k=1 VDAT05: Doshi and Agrawal

  16. Similarity Metrics VDAT05: Doshi and Agrawal

  17. Independence Collapsing VDAT05: Doshi and Agrawal

  18. Independence Collapsing 11 4 11 3 0 1,8 1 5,11,7 5,11 5 3,9,2 3,9 3 4,6,10 4,6 4 11 0 4 6 Similarity index for fault F for each existing node i: Max. SIM (F, kth fault of node i) where k = 1…..K, and K is number of faults in node i. VDAT05: Doshi and Agrawal

  19. Concurrent test generation for C17 2-1 4-1 a x 5-1 1-1 b 3-1 7-1 c 11-1 y d 6-1 10-1 9-1 e 8-1 VDAT05: Doshi and Agrawal

  20. Results (ALU – 74181) VDAT05: Doshi and Agrawal

  21. Conclusions and Future Work • Faults are reclassified into four classes: • Equivalent • Dominant • Independent • Concurrently-testable (also called compatible in the literature) • A new fault collapsing algorithm based on Independent Faults is introduced. • This algorithm frequently collapses the graph into a minimal clique. • This work motivates the need for ATPG algorithms for concurrent fault targets. • The problem of completely determining all edges of the independence graph is complex. • The algorithm needs to be extended for incompletely – specified independence graph. VDAT05: Doshi and Agrawal

  22. Thank You! VDAT05: Doshi and Agrawal

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