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ECE 553: TESTING AND
TESTABLE DESIGN OF
DIGITAL SYSTES
Combinational ATPG
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Overview
Major ATPG algorithms
•
Definitions
•
DAlgorithm (Roth)  1966
–
Dcubes
–
Bridging faults
–
Logic gate function change faults
•
PODEM (Goel)  1981
–
XPathCheck
–
Backtracing
•
Summary
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Forward Implication
•
Results in logic gate inputs that are
significantly labeled so that output
is uniquely determined
•
AND gate forward implication
table:
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Backward Implication
•
Unique determination of all gate inputs when the gate
output and some of the inputs are given
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Implication Stack, Decision Tree, and Backtrack
0
1
0
0
0
0
0
1
1
1
1
E
F
B
1
Unexplored
Present Assignment
Searched and Infeasible
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Objectives and Backtracing in ATPG
•
Objective
– desired signal value goal for ATPG
–
Guides it away from infeasible/hard solutions
–
Uses heuristics
•
Backtrace
– Determines which primary input and
value to set to achieve objective
–
Use heuristics such as nearest PI
•
Forward trace
–
Determines gate through which the
fault effect should be sensitized
–
Use heuristics such as output that is closest to the present
fault effect
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BranchandBound Search
•
Efficiently searches binary search tree
•
Branching
– At each tree level, selects which input
variable to set to what value
•
Bounding
– Avoids exploring large tree portions by
artificially restricting search decision choices
–
Complete exploration is impractical
–
Uses
heuristics
•
Backtracking
– Search fails, therefore undo some of the
work completed and start searching from a location
where search options still exist
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DAlgorithm – Roth (1966)
•
Fundamental concepts invented:
–
First complete ATPG algorithm
–
DCube
–
DCalculus
–
Implications
– forward and backward
–
Implication stack
–
Backtrack
–
Test Search Space
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Singular Cover Example
•
Minimal set of logic signal assignments to represent a function
–
show
prime implicants and prime implicates
of
Karnaugh
map
(with explicitly showing the outputs too)
Gate
AND
1
2
3
Inputs
A
0
X
1
B
X
0
1
Output
d
0
0
1
Gate
NOR
1
2
3
Inputs
1
X
0
e
X
1
0
Output
F
0
0
1
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Primitive DCube of Failure
•
Models circuit faults:
–
Stuckat0
–
Stuckat1
–
Other faults, such as
Bridging fault
(short circuit)
–
Arbitrary change in logic function
•
AND Output sa0:
“
1
1
D
”
•
AND Output sa1:
“
0
X
D
”
“
X
0
D
”
•
Wire sa0:
“
D
”
•
Propagation Dcube
– models conditions under
which fault effect propagates through gate
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Construction of Primitive
DCubes of Failure
1. Make cube set
a
1
when good machine output
is
1
and set
a
0
when good machine output is
0
2. Make cube set
b
1
when failing machine output
is
1
and
b
0
when it is
0
3. Change
a
1
outputs to
0
and Dintersect each
cube with every
b
0
.
If intersection works,
change output of cube to
D
4. Change
a
0
outputs to
1
and Dintersect each
cube with every
b
1
.
If intersection works,
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 Winter '08
 ece553
 Algorithms, Gate, ATPG, propagation dcube

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