independence fault collapsing
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
Aug.13, 2005 VDAT05: Doshi and Agrawal 1
Independence Fault Collapsing
Auburn University, Department of Electrical and Computer Engineering Auburn, AL 36849, USA
Alok S. Doshi (Speaker)Vishwani D. Agrawal
Aug.13, 2005 VDAT05: Doshi and Agrawal 2
Outline
• Motivation
• Fault Classification
• Independence Graph and Matrix
• Independence Fault Collapsing
• Concurrent Test Generation
• Conclusions and Future Work
Aug.13, 2005 VDAT05: Doshi and Agrawal 3
Motivation
ATPG Tests
Hitec1 10
Fastest2 7
Gentest3 7
1 T. 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.
C17 - ISCAS85 Benchmark Circuit
a
b
cd
e
x
y
Minimum 4
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Fault Classification
T(F 1 )
T(F 1 ) T(F 1 )
T(F 2 )
T(F 2 ) T(F 2 )
(a) F 1 and F 2 ar e e qui val e nt . (b) F 1 do m i nate s F 2 .
(c ) F 1 and F 2 ar e i nde pe nde nt . (d) F 1 and F 2 ar e c o nc ur r e nt l y te s tabl e .
T(F 1 ) = T(F 2 )
Aug.13, 2005 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.
Aug.13, 2005 VDAT05: Doshi and Agrawal 6
Structural Independences
sa1sa1
sa1
sa1
sa1
sa1
sa1
sa0
sa0
sa0
sa0
sa0
sa0
sa0 sa0
sa0
sa0
sa1
sa1
sa1
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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.
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Functional Independences
C UTC 0
C UTC 0
C UT(Fi)C i
C UTC 0
C UTC 0
C UT(Fi)C i
Prim a ryI n pu ts
Prim a ryI n pu ts
Prim a ryO u tpu tsPrim a ry
O u tpu t
R e du n da n t fa u lt s Fj a rein de pe n de n t o f F i
R e du n da n t fa u lt s Fj a rein de pe n de n t o f F i
(a ) F in din g a ll fa u lt s in de pe n de n t o f F i in a s in g le o u tpu t c ircu it . (b) F in din g a ll fa u lt s in de pe n de n t o f F i in a m u lt iple o u tpu t c ircu it .
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Example Circuit2-1
4-1
1-1
6-1
8-1
7-13-1
9-1
5-1
10-1
11-1
a
b
cd
e
x
y
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.
Aug.13, 2005 VDAT05: Doshi and Agrawal 10
Independence Matrix and Graph
F 1 2 3 4 5 6 7 8 9 10 11
1 0 1 1 1 1 1 0 0 1 0 1
2 1 0 0 1 1 0 1 0 0 0 1
3 1 0 0 0 1 1 1 1 0 1 1
4 1 1 0 0 1 0 1 0 0 0 1
5 1 1 1 1 0 0 0 1 1 1 0
6 1 0 1 0 0 0 1 1 1 0 0
7 0 1 1 1 0 1 0 1 1 0 0
8 0 0 1 0 1 1 1 0 1 1 1
9 1 0 0 0 1 1 1 1 0 1 1
10 0 0 1 0 1 0 0 1 1 0 1
11 1 1 1 1 0 0 0 1 1 1 0
1 2 3 4 5
6 7 8 9 1 0
11
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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.
Aug.13, 2005 VDAT05: Doshi and Agrawal 12
Cliques
1 2 3 4 5
6 7 8 9 1 0
11
1 2 3 4 5
6 7 8 9 1 0
11
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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 NN
j=1 i=1
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Degree of IndependenceFault 1 2 3 4 5 6 7 8 9 10 11 DI
1 0 1 1 1 1 1 0 0 1 0 1 7
2 1 0 0 1 1 0 1 0 0 0 1 5
3 1 0 0 0 1 1 1 1 0 1 1 7
4 1 1 0 0 1 0 1 0 0 0 1 5
5 1 1 1 1 0 0 0 1 1 1 0 7
6 1 0 1 0 0 0 1 1 1 0 0 5
7 0 1 1 1 0 1 0 1 1 0 0 6
8 0 0 1 0 1 1 1 0 1 1 1 7
9 1 0 0 0 1 1 1 1 0 1 1 7
10 0 0 1 0 1 0 0 1 1 0 1 5
11 1 1 1 1 0 0 0 1 1 1 0 7
DI 7 5 7 5 7 5 6 7 7 5 7
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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
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Similarity Metrics
Fault 1 2 3 4 5 6 7 8 9 10 11
1 0 11 11 11 11 11 3 4 11 4 11
2 11 0 4 11 11 6 11 6 4 6 11
3 11 4 0 4 11 11 11 11 0 11 11
4 11 11 4 0 11 6 11 6 4 6 11
5 11 11 11 11 0 4 3 11 11 11 0
6 11 6 11 6 4 0 11 11 11 4 4
7 3 11 11 11 3 11 0 11 11 5 3
8 4 6 11 6 11 11 11 0 11 11 11
9 11 4 0 4 11 11 11 11 0 11 11
10 4 6 11 6 11 4 5 11 11 0 11
11 11 11 11 11 0 4 3 11 11 11 0
Aug.13, 2005 VDAT05: Doshi and Agrawal 17
Independence CollapsingFault 1 3 5 8 9 11 7 2 4 6 10 DI
1 0 1 1 0 1 1 0 1 1 1 0 7
3 1 0 1 1 0 1 1 0 0 1 1 7
5 1 1 0 1 1 0 0 1 1 0 1 7
8 0 1 1 0 1 1 1 0 0 1 1 7
9 1 0 1 1 0 1 1 0 0 1 1 7
11 1 1 0 1 1 0 0 1 1 0 1 7
7 0 1 0 1 1 0 0 1 1 1 0 6
2 1 0 1 0 0 1 1 0 1 0 0 5
4 1 0 1 0 0 1 1 1 0 0 0 5
6 1 1 0 1 1 0 1 0 0 0 0 5
10 0 1 1 1 1 1 0 0 0 0 0 5
DI 7 7 7 7 7 7 6 5 5 5 5
Aug.13, 2005 VDAT05: Doshi and Agrawal 18
Independence Collapsing
1
3
51,8
3,9
5,115,11,7
3,9,2 44,64,6,10
11
11
4 11
0
03
4 6
F 1 3 5 8 9 11 7 2 4 6 10
1 0 11 11 4 11 11 3 11 11 11 4
3 11 0 11 11 0 11 11 4 4 11 11
5 11 11 0 11 11 0 3 11 11 4 11
8 4 11 11 0 11 11 11 6 6 11 11
9 11 0 11 11 0 11 11 4 4 11 11
11 11 11 0 11 11 0 3 11 11 4 11
7 3 11 3 11 11 3 0 11 11 11 5
2 11 4 11 6 4 11 11 0 11 6 6
4 11 4 11 6 4 11 11 11 0 6 6
6 11 11 4 11 11 4 11 6 6 0 4
10 4 11 11 11 11 11 5 6 6 4 0
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.
Aug.13, 2005 VDAT05: Doshi and Agrawal 19
Concurrent test generation for C17
Fault Targets Test
(a b c d e)
1,8 10010
3,9,2 01111
5,11,7 X1010
4,6,10 10101
2-14-1
1-1
6-1
8-1
7-13-1
9-1
5-1
10-1
11-1
a
b
cd
e
x
y
Aug.13, 2005 VDAT05: Doshi and Agrawal 20
Results (ALU – 74181)Node Number of faults Test vectorsno. Total Targeted Detected from Cumulative
this
nodeothernodes
coverage
1 5 5 5 6 11 010011110100012 3 3 3 2 16 010011111101013 8 7 7 3 26 010111010000014 3 3 3 3 32 101x01010100005 5 3 3 4 39 101001010110006 6 6 6 2 47 111110000010017 7 4 4 3 54 111000001000008 14 11 11 1 66 111001101010119 8 6 5 1 72 10010100110101
10 8 4 3 2 77 1x10101110110011 8 3 3 1 81 0101000010110012 9 2 2 1 84 1x011110001100
Aug.13, 2005 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.
Aug.13, 2005 VDAT05: Doshi and Agrawal 22
Thank You!