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Diagnostic and Detection Fault Collapsing for
Multiple Output Circuits
Raja K. K. R. Sandireddy and Vishwani D.
Agrawal Dept. Of Electrical and Computer
Engineering, Auburn University, Auburn, AL-36849
USA.
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Outline

• Introduction
• Fault Equivalence and Fault Dominance
• Functional collapsing
• Fault Equivalence and Dominance definitions
• Results of functional collapsing
• Hierarchical fault collapsing
• Conclusions and Future work.

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Equivalence
R Structural equivalence1 Two faults f1 and f2
are said to be R structurally equivalent if they
produce the same reduced circuit graph netlist
when faulty values are implied and constant edges
signals are removed. Functional equivalence1
Two faults f1 and f2 are said to be functionally
equivalent if they modify the Boolean function of
the circuit in the same way, i.e., they yield the
same output functions.
1 E. J. McCluskey and F. W. Clegg, Fault
Equivalence in Combinational Logic Networks,
IEEE Trans. Computers, vol. C-20, no. 11, Nov.
1971, pp. 1286-1293.
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Structural Dominance

• A fault fi is said to dominate fault fj if the
  faults are equivalent with respect to test set of
  fault fj.

a
a
0
1
c
c
1
0
Equivalence collapsed set a0, b0, c0,
c1 Dominance collapsed set a0, b0, c1
b
b
0
1
Example Full adder circuit. Total faults
60 Structural equivalence collapsed set2, 3 38
(0.63) Structural dominance collapsed set3 30
(0.5)
2 Using Hitec, 3 Using Fastest
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Functional Dominance4
F1
1
Z
F0
0
1
F2
If the fault introduced in block F1 dominates the
fault in block F2, then Z is always 0.
For the full adder, functional dominance
collapsed set 12 (0.20) Structural equiv.
38, Structural dom. 30, Functional equiv. 23
4 V. D. Agrawal, A. V. S. S. Prasad, and M. V.
Atre, Fault Collapsing via Functional
Dominance, Proc. International Test Conf., 2003,
pp. 274-280.
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Equivalence Definitions

• For multiple output circuits,
• Diagnostic Equivalence - Two faults of a Boolean
  circuit are called diagnostically equivalent if
  and only if the functions of the two faulty
  circuits are identical at each output.
• Detection Equivalence - Two faults are called
  detection equivalent if and only if all tests
  that detect one fault also detect the other
  fault, not necessarily at the same output.

The faults c0 and Y0 are detection equivalent
faults, but not diagnostic equivalent.
For the full adder, diagnostic equivalence
collapsed set 26 (0.43), detection
equivalence collapsed set 23 (0.38) Structural
equiv. 38, Structural dom. 30, Functional
equiv. 26, Functional dom. 12
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Dominance Definitions

• Fault Dominance5 - A fault fi is said to dominate
  fault fj if (a) the set of all vectors that
  detects fault fj is a subset of all vectors that
  detects fault fi and (b) each vector that detects
  fj implies identical values at the corresponding
  outputs of faulty versions of the circuit.
• Conventionally dominance is defined as
• A fault fi is said to dominate fault fj if the
  faults are equivalent with respect to test set of
  fault fj.
• If all tests of fault fj detect another fault fi,
  then fi is said to dominate fj.

5 J. F. Poage, Derivation of Optimum Tests to
Detect Faults in Combinational Circuits", Proc.
Symposium on Mathematical Theory of Automata,
1962, pp. 483-528.
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Dominance Definitions contd.

• For multiple output circuits, the two possible
  interpretations of dominance
• Diagnostic dominance - If all tests of a fault f1
  detect another fault f2 on the exact same outputs
  where f1 was detected, then f2 is said to
  diagnostically dominate f1.
• Detection dominance - If all tests of a fault f1
  detect another fault f2, irrespective of the
  output where f1 was detected, then f2 is said to
  detection dominate f1 .
• Diagnostic dominance implies detection dominance.
• For the full adder, diagnostic dominance
  collapsed set 12 (0.2)
• detection dominance collapsed set 6
  (0.1)
• Structural equiv. 38, Structural dom. 30,
  Diagnostic equiv. 26,
• Detection equiv. 23

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Results Functional Collapsing
2 Using Hitec (obtained from Univ. of Illinois at
Urbana-Champaign) 3 Using Fastest (obtained from
Univ. of Wisconsin at Madison) 4 Agrawal et al.
ITC03
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Results Test Vectors
Test vectors obtained using Gentest ATPG6.
6 W. T. Cheng and T. J. Chakraborty, Gentest An
Automatic Test Generation System for Sequential
Circuits, Computer, vol. 22, no. 4, pp. 4349,
April 1989.
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Hierarchical Fault Collapsing
Total Faults Full Adder 60, 64-bit Adder
3714, 1024-bit Adder 59394, c4321116,
c4992646
Detection collapsing can be used only for those
sub-circuits whose outputs are POs at the
top-level.
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CPU time (sec) for hierarchical collapsing
Flattened (Hitec)
Flattened (Our Program)
Hierarchical (two-level)
Hierarchical (multi-level)
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Conclusions

• Diagnostic and detection collapsing should be
  used only with smaller circuits.
• Collapse ratios using detection dominance
  collapsing is about 10-20.
• Hierarchical fault collapsing
• Better (lower) collapse ratios due to functional
  collapsed library
• Order of magnitude reduction in collapse time.
• Smaller fault sets
• Fewer test vectors
• Reduced fault simulation effort
• Easier fault diagnosis.
• Use caution when using dominance collapsing!!

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Future Work

• Generate fault collapsing library of standard
  cells (Mentor Graphics, etc.).
• Efficient redundancy detection program.
• Customized ATPG to obtain minimal test vector set.