Computer Engineering, KFUPM
Test Set Compaction for Sequential
Circuits based on Test Relaxation
M.S Thesis Defense
S. Saqib Khursheed
Advisor: Dr. Aiman H. El-Maleh
Members: Dr. Sadiq M. Sait & Dr. Alaaeldin Amin
29th Dec 04
Computer Engineering, KFUPM
Outline
•
•
•
•
•
•
Motivation
State of the Art Static Compaction Algorithms
Test Relaxation Algorithm
Proposed Algorithms and Experimental Results
Limitations of Justification algorithm
Conclusion & Future Work
2
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Motivation
• Compaction is the process of reducing the size of test
set while maintaining the fault-coverage.
• To overcome High Complexity of Sequential ATPGs
• To reduce Test Application Time  reduced cost!
• To overcome Memory Limitations of the Tester.
3
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Types of Compaction Algorithms
• Static Compaction  Compaction Algorithms are
applied as a post-processing step to test generation
process.
• Dynamic Compaction  Compaction Algorithms are
incorporated in test generation process.
• Static Compaction is more useful than Dynamic
Compaction in Sequential Circuits.
4
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State-of-the-art Static Compaction
Algorithms
• Some of the popular algorithms include:
– Vector Restoration
• Linear Reverse Order Restoration (LROR)
• Radix Reverse Order Restoration (RROR)
• SIngle FAult Restoration (SIFAR)
• Mixed Mode (MISC)
• SECO
– Subsequence Merging
– State Traversal based on Relaxed States
5
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LROR
Snapshot of
algorithm under
execution
Restoring
Targeting
Restoringfvector
11 and f2..#Restoring
4, 5 and 6,
vector
detects#6
#the
5doesn’t
and
fault
6, fdoesn’t
1detect
and f2.the
fault
detect the faults
f1 and f2 detected
Restored vector # 4, 5 and 6,
are concatenated with
previously restored test
vectors .
6
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State-Traversal
7
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Important Attributes of Static
Compaction Algorithms
• Test sequences for Hard-to-Detect faults (HTDF) can
easily detect Easy-to-Detect faults (ETDF).
• State Traversal eliminates redundant vectors
• Merging of relaxed Subsequences adds another level
of freedom to test compaction.
• Increasing the Fault coverage fuels compaction.
8
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Test Relaxation Algorithm
• Restoration algorithms rely on vector-by-vector fault
simulation to extract the test sequence.
• Recently, an efficient Test Relaxation technique has been
proposed to extract the necessary assignments for detecting
the faults.
• Our algorithms (discussed next) rely on test relaxation
algorithm for extracting the self-initializing subsequence.
• A relaxed test set facilitates Subsequence Merging and
State Traversal.
9
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Proposed Algorithms
• Following algorithms are proposed:
– Linear Reverse Order Restoration
• with State Traversal
• with State Traversal-2
– Merging Restoration
– Hybrid Schemes
• Hybrid-I
• Hybrid-II
– Fault-Coverage based Compaction
• FC-LROR
• FC-MR
10
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Reverse Order Restoration with State Traversal
using Relaxed Test Set
After first pass of fault
Start from last time frame
simulation, information is
having un-justified fault.
stored
Justification of faults f4,
f5. Self-initialized
subsequence is found by
relaxation algorithm.
f4 and f5 detected
State Traversal may
further reduce the size of
Reduced subsequence
subsequence
f4 and f5 detected
Re-current states, removal of time
frames is possible
11
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Reverse Order Restoration with State Traversal
using Relaxed Test Set
0/1
1/x
1/0
Fault Simulate the subsequence
and drop all the faults detected
f4, f5, f1 and f2 are detected
Dropping detected faults leaves f3
The above steps are repeated
Fault # 3 is justified.
0/x
1/x
x/0
Concatenation with previously
justified test vectors.
Test Set after Compaction
detecting all the faults.
12
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Motivation behind ST-2
STRATEGATE Test Sequences
LROR
LROR-ST
Ckt
TS
TS (sec)
TS (sec)
s298
194
152 (0.06)
134 (0.06)
s344
86
44 (0.03)
44 (0.09)
s641
166
133 (0.07)
157 (0.11)
s713
176
115 (0.07)
134 (0.1)
s820
590
469 (0.27)
466 (0.39)
s832
701
534 (0.31)
470 (0.42)
s1196
574
268 (0.3)
268 (0.35)
s1238
625
268 (0.33)
268 (0.37)
s1488
593
466 (0.56)
479 (0.71)
s1494
540
453 (0.52)
401 (0.7)
s5378
11481
760 (45.34)
726 (45.34)
s35932
257
131 (20.8)
131 (21.12)
Total (sec)
15983
3793 (68.66)
3678 (69.76)
13
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Merging Restoration
• Merging algorithm follows the same flow as the
previous algorithm.
• Instead of concatenation of subsequences, relaxed
subsequences are merged with previously restored
subsequences.
• Merging towards bottom
• Merging towards top
14
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Merging towards Bottom
11xx
0x01
11xx
X
X
0x01
10x1
1011
xxx0
11x0
00x1
0011
11xx
11xx
1011
11x0
001x
Merged
Compact Test
Set Subsequence
Newly Restored Subsequence
15
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Exp. Results
STRATEGATE Test Sequences
ITE
ITE
LROR [14]
MR
LROR
LROR-ST
LROR_ST2
LROR [14]
LROR_ST2
Ckt
TS
TS (sec)
TS (sec)
TS (sec)
TS (sec)
TS (sec)
TS (sec)
TS (sec)
s298
194
138 (0.14)
154 (0.05)
152 (0.09)
134 (0.06)
152 (0.11)
112 (0.74)
152 (0.15)
s344
86
62 (0.09)
61 (0.04)
44 (0.1)
44 (0.09)
44(0.1)
51 (0.18)
44 (0.13)
s641
166
118 (0.13)
148 (0.59)
133 (0.07)
157 (0.11)
119 (0.17)
117 (0.32)
118 (0.56)
s713
176
139 (0.16)
140 (0.54)
115 (0.07)
134 (0.1)
112 (0.25)
103 (0.61)
111 (0.49)
s820
590
489 (0.79)
531 (3.11)
469 (0.64)
466 (0.39)
456 (0.59)
471 (1.94)
428 (1.96)
s832
701
543 (0.89)
568 (3.31)
534 (0.45)
470 (0.42)
498 (0.6)
443 (4.5)
460 (2.28)
s1196
574
277 (0.28)
242 (1.79)
268 (0.59)
268 (0.35)
268 (1.17)
260 (1.2)
266 (1.21)
s1238
625
285 (0.31)
248 (2.18)
268 (0.62)
268 (0.37)
268 (1.23)
270 (1.09)
266 (1.64)
s1488
593
501 (1.79)
533 (5.38)
466 (0.56)
479 (0.71)
453 (1.01)
474 (14.89)
423 (4.0)
s1494
540
468 (1.71)
501 (4.82)
453 (0.67)
401 (0.7)
434 (0.88)
422 (21.92)
434 (2.39)
s5378
11481
677 (38.71)
1549 (227.57)
760 (45.34)
726 (45.34)
710 (51.8)
585 (71.55)
703 (74.46)
s35932
257
137 (56.93)
188 (389.7)
131 (20.8)
131 (21.12)
131 (22.5)
137 (119.76)
125 (128.66)
Total (sec)
15983
3834 (101.9)
4863 (639.1)
3793 (68.66)
3678 (69.76)
3645 (80.41)
3445 (238.7)
3530 (217.95)
3
9
10
9
Better
16
5
Computer Engineering, KFUPM
Merging Restoration
Number of SS restored
MR
LROR-ST2
Ckts
# of SS
# of SS
s298
8
6
s344
18
6
s641
65
9
s713
72
15
s820
87
29
s832
88
25
s1196
192
147
s1238
207
150
s1488
65
16
s1494
62
16
s5378
132
49
s35932
35
7
Total
1031
475
17
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Hybrid Schemes
• LROR suffers from quick saturation.
• Hybrid schemes are proposed to address this
limitation of LROR.
• Hybrid-I uses Test Relaxation and random filling to
change the composition of the test.
• This helps moving the algorithm out of local-minima
and search space is therefore increased.
18
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Hybrid Schemes
3+
Hybrid-I
2+
LROR-ST2
Test
Relaxation
19
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Hybrid Schemes
Hybrid-II
1+
Hybrid-I
MR
20
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Hybrid Schemes
STRATEGATE Test Sequences
ITE
ITE
ITE
ITE
ITE
LROR [12]
SIFAR [13]
MISC [12]
Hyb-I
Hyb-II
Ckt
TS
TS (sec)
TS (sec)
TS (sec)
TS (sec)
TS (sec)
s298
194
125 (0.6)
112 (0.4)
98 (3.2)
106 (0.96)
89 (1.16)
s344
86
47 (0.1)
48 (0.2)
43 (0.4)
48 (0.26)
48 (0.31)
s641
166
78 (0.5)
87 (0.4)
63 (1.7)
68 (1.48)
68 (1.64)
s713
176
72 (0.6)
94 (1.1)
60 (0.8)
64 (1.37)
64 (1.54)
s820
590
394 (6.4)
388 (6.5)
335 (15.2)
377 (18.1)
376 (22)
s832
701
458 (8.8)
435 (4.5)
368 (14.0)
418 (18.9)
406 (24.3)
s1196
574
221 (1.7)
237 (3.4)
216 (3.2)
213 (37.4)
182 (41.5)
s1238
625
222 (2.6)
251 (1.5)
222 (3.6)
222 (33.1)
196 (36.6)
s1488
593
343 (27.1)
312 (8.8)
364 (39.4)
362 (17.4)
361 (24.5)
s5378
11481
711 (339.4)
597 (89.5)
583 (2148)
637 (307.4)
637 (383.7)
s35932
257
110 (752.3)
152 (290)
101 (1177)
133 (875.76)
133 (1002.7)
Total (sec)
15443
2781 (1140.1)
2713 (406.3)
2453 (3406.5)
2648 (1326.6)
2560 (1539.9)
Better
Equal
78
1
88
42
6
1
1
5
21
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Hybrid Schemes
HITEC Test Sequences
ITE
ITE
ITE
ITE
LROR [12]
MISC [12]
Hyb-I
Hyb-II
Ckt
TS
TS (sec)
TS (sec)
TS (sec)
TS (sec)
s298
322
109 (0.8)
97 (1.1)
161 (0.87)
143 (0.98)
s344
127
47 (0.1)
47 (0.5)
45 (0.5)
45 (0.53)
s641
209
63 (1.0)
72 (1.2)
66 (2.15)
66 (2.28)
s713
173
74 (0.7)
74 (1.0)
71 (1.6)
71 (1.77)
s820
1115
578 (13.8)
432 (28.3)
489 (24)
488 (27.4)
s832
1137
562 (8.3)
383 (64.0)
497 (17.7)
493 (20.5)
s1196
435
226 (2.3)
223 (2.5)
214 (35.6)
187 (38.8)
s1238
475
227 (1.9)
225 (1.9)
218 (42.7)
184 (51.8)
s1488
1170
571 (10.4)
572 (354.6)
650 (40.4)
648 (49.6)
s5378
912
245 (108.1)
271 (189.0)
262 (90.8)
262 (107.3)
s35932
496
142 (227.8)
117 (1158)
187 (1020.8)
145 (1379.6)
s3271
709
555 (24.6)
443 (265.0)
682 (54.6)
369 (103.2)
s3384
161
104 (11.6)
92 (13.1)
104 (17.3)
75 (20.1)
s4863
518
302 (20.5)
315 (25.6)
272 (379.8)
133 (430.1)
Total (sec)
7959
3840 (431.9)
3363 (2105.8)
3918 (1728.9)
3309 (2233.6)
Better
Equal
79
1
9 6
10
4
22
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Fault-Coverage based Compaction
• Motivation: A large reduction in test size is possible
by increasing the fault coverage of currently restored
subsequences.
• This is achieved by relaxing and randomly filling the
restored SS.
• Fault coverage (FC) based compaction:
– LROR based on increasing the FC  FC-LROR
– MR based on increasing the FC  FC-MR
23
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Fault-Coverage based Compaction
IDEA
LROR
FC-LROR
24
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FC-LROR
Currently Compacted Test
Und Faults?
New SS
No
End
Yes
Test Relaxation
n
25
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FC-MR
Fully Specified
New SS
Test Relaxation for all
und. faults
Merging towards Top
Currently Compacted Test
Und Faults?
No
End
Yes
Random Filling &
Test Relaxation
n
26
Computer Engineering, KFUPM
Exp. Results: FC-based Compaction
HITEC Test Sequences
Ckt
TS
SECO [37]
SIFAR [13]
LROR [12]
FC-LROR
MR
FC-MR
MISC [12]
s298
322
216
129
169
157
207
175
139
s344
127
61
50
47
47
69
59
48
s641
209
125
112
105
88
158
81
102
s713
173
106
93
89
77
129
72
88
s820
1115
790
599
598
574
863
709
496
s832
1137
779
597
605
568
879
694
484
s1196
435
281
256
251
250
255
213
252
s1238
475
303
272
266
263
269
228
267
s1488
1170
828
613
647
705
911
711
643
s1494
1245
855
640
630
668
974
781
605
s5378
912
653
456
300
330
706
357
292
Total
7320
4997
3817
3707
3727
5420
4080
3416
All
84
74
All
7
54
Better
Equal
1
27
Computer Engineering, KFUPM
Exp. Results: FC-based Compaction
STRATEGATE Test Sequences
Ckt
TS
LROR [14]
SIFAR [13]
LROR [12]
MR
FC-MR
FC-LROR
MISC [12]
s298
194
138
116
125
154
141
150
123
s344
86
62
48
47
61
50
41
44
s641
166
118
87
91
148
79
101
74
s713
176
139
125
112
140
87
86
92
s820
590
489
423
401
531
497
392
356
s832
701
543
511
475
568
509
465
375
s1196
574
277
251
234
242
199
241
234
s1238
625
285
251
244
248
212
245
244
s1488
593
501
390
363
533
591
433
370
s1494
540
468
408
417
501
460
413
417
s5378
11481
677
597
734
1549
809
608
704
Total
15726
3697
3207
3243
4675
3634
3175
3033
10
7
65
64
Better
All
10
7
34
28
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Hybrid-FC-LROR
2+
FC-LROR
1+
MR
29
Computer Engineering, KFUPM
Exp. Results: Hybrid-FC-LROR
STRATEGATE Test Sequences
Circuit
TS
ITE
LROR [12]
S298
194
125
112
98
95
S344
86
47
48
43
38
S641
166
78
87
63
59
S713
176
72
94
60
45
S820
590
394
388
335
347
S832
701
458
435
368
366
S1196
574
221
237
216
180
S1238
625
222
251
222
192
S1488
593
343
312
364
380
S1494
540
297
313
296
362
S5378
11481
711
597
583
561
Total
15983
2968
2874
2648
2625
9
9
8
Better
ITE
SIFAR [13]
ITE
MISC[12]
ITE
Hyb-FC-LROR
30
Computer Engineering, KFUPM
Exp. Results: Hybrid-FC-LROR
HITEC Test Sequences
ITE
ITE
ITE
Ckt
TS
LROR [12]
MISC [12]
Hyb-FC-LROR
s298
322
109
97
96
s344
127
47
47
44
s641
209
63
72
60
s713
173
74
74
57
s820
1115
578
432
403
s832
1137
562
383
379
s1196
435
226
223
182
s1238
475
227
225
188
s1488
1170
571
572
586
s1494
1245
540
492
462
s5378
912
245
271
215
s3271
709
555
443
351
s3330
578
219
218
188
s3384
161
104
92
56
s4863
518
302
315
136
Total
9286
4422
3956
3403
31
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Limitations of Justification Algorithm
• Justification of G/F value is done based on cost
functions, which is an approximate method.
• Cost of Good value is only used.
• These limitations result in extraction of longer test
sequences than necessary.
32
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Conclusion & Future Work
• In this work, we have proposed several efficient static
compaction techniques, which achieve the following:
– Better or comparable level of compaction while reducing the
runtime.
– All important attributes of static compaction techniques are
integrated.
– Limitation of quick saturation of Restoration based
techniques has been addressed.
– A new class of compaction algorithms has been introduced,
based on increasing the fault-coverage of restored
subsequences.
33
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Conclusion & Future Work
• Investigate techniques to overcome the limitations of
Justification Algorithm.
• Investigate techniques for increasing the fault
coverage of an extracted Subsequences.
34
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Thank
you!
Q &A
35
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Backup Slides
36
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Types of Compaction Algorithms
• Unique opportunities provided by Static Compaction:
– It may be applied to test vectors generated by any
ATPG tool without modifying the test generation
process.
– It may be applied after dynamic compaction.
– It takes lesser time to get final test set.
– The shortest test sequence for sequential circuits are
generated by static compaction techniques.
• For these reasons, Static Compaction is more popular in
Sequential circuits than Dynamic Compaction.
37
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Modified LROR
38
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State-of-the-art Static Compaction
Algorithms (SIFAR)
• SIFAR uses the basic idea of Test Vector Restoration.
• It considers a single target fault (in decreasing order of
detection time) and restores test vectors until fault is
detected.
– This is also called Test Vector Restoration.
• SIFAR uses parallel fault simulator to speed up the
restoration process.
39
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SIFAR
Snapshot of
algorithm under
execution
1. Restoring
Targeting
Restoringfvector
1.
# 4, 5vector
and 6,
#6
detect
faultthe
#detects
5doesn’t
and 6,
thedoesn’t
fault fthe
1.detect
fault
F1 detected
Restored vector # 4, 5 and 6,
are concatenated with
previously restored test
vectors .
40
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State-of-the-art Static Compaction
Algorithms (RROR)
• RROR is a variation of LROR, meant to speed up the
restoration process.
• In RROR, rather than restoring frame by frame, the
algorithm jumps to previous time frames.
• Radix Search is based on binary search and depends
on the value of ri-1, such that, 1< r ≤ 2 and i=1,2,3..
• The algorithm keeps jumping until the target fault(s) is
detected.
41
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RROR
Snapshot of
algorithm under
execution
Targeting
1 and f2.# Restoring
Restoringfvector
7, 4,
3,
8 and
5 and
9,
vector
#9detect
doesn’t
doesn’t
6,
detects
the faults
thedetect
fault
f1 and
fthe
1 and
f2.
fault.
r=2,
i=1
f2. r=2,
r=2,
i=3i=2
f1 and f2 detected
Restored vector # 3, 4 … 9,
are concatenated with
previously restored test
vectors .
42
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Merging Restoration
• A newly restored subsequence may be merged with
previous subsequences either towards Top or Bottom
or from where the savings are highest.
• Merging towards bottom  starts from top and slides
the newly restored SS downwards until merged or
appended.
• Merging towards TOP  starts from Bottom and
slides the newly restored SS upwards until merged or
appended
43
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Fault-Coverage based Compaction
• Observations: Initially restored test sequences cover a
large number of faults. This is called covering effect,
which is used by Restoration based compaction
algorithms.
• Motivation: A large reduction in test size is possible
by increasing the fault coverage of currently restored
subsequences.
44