1. A Static Test Compaction Technique for Combinational Circuits Based on Independent Fault Clustering Yahya E. Osais & Aiman H. El-Maleh King Fahd University of Petroleum & Minerals, Computer Engineering Department, Dhahran 31261, Saudi Arabia {yosais,aimane}@ccse.kfupm.edu.sa

2. 2 Outline Motivation Research problem & contribution Taxonomy of static compaction algorithms Test vector decomposition Independent fault clustering Experimental results Conclusion

3. 3 Motivation Rapid advancement in VLSI led to SoC. Testing SoCs requires large amount of data. Impact on testing time & memory requirements of test equipment. Challenges: –Reduce amount of test data. –Reduce time a defective chip spends on a tester.

4. 4 Research Problem & Contribution Static compaction for combinational circuits.Static compaction for combinational circuits. –Reduce the size of a test set as much as possible. ContributionsContributions –Test vector decomposition. Test vector can be eliminated if its components can be moved to other test vectors. –Efficient static compaction algorithm. Independent fault clustering.

5. 5 Taxonomy of Static Compaction Algorithms Static Compaction Algorithms for Combinational Circuits Redundant Vector Elimination Test Vector Addition & Removal Test Vector Modification Set Covering Test Vector Reordering Essential Fault Pruning Based on ATPG Essential Fault Pruning Based on ATPG Merging Based on Relaxation Based on Raising Test Vector Decomposition IFC CBCGraph Coloring

6. 6 Test Vector Decomposition Decompose a test vector into its atomic components. Employ relaxation per a fault. t p = 010110 & F p = {f 1,f 2,f 3 } –(f 1,01xxxx) –(f 2,0x01xx) –(f 3,x1xx10) Compaction modeled as graph coloring.

7. 7 Independent Fault Clustering Preliminaries Two faults are independent if they cannot be detected by a single test vector. Two faults are compatible if their components are compatible. A set of faults is independent (IFS) if no two faults can be detected by the same test vector. A set of faults is compatible (CFS) if all faults can be detected by the same test vector.

8. 8 Independent Fault Clustering Algorithm Description Fault simulate T without fault dropping. Match essential faults: –Extract atomic component c f from t. –Map to c f CFS. Find IFSs. Match remaining faults: –Extract atomic component c f from t  T f. –Map c f to CFS.

9. 9 Independent Fault Clustering Illustrative Example Fault ComponentFault DetectedTest Vector xxx1xx0xxxf1f1 0xx11x0x10v1v1 0xxx1xxxx0f2f2 0xxxxx0x10fe3fe3 x0x1xxxxxxf1f1 10x1xxxx00v2v2 1xxxxxxx00fe4fe4 10x1xxxxxxfe5fe5 0xx0xxxxxxfe6fe6 0xx0xxx00xv3v3 xxxxxxx00xfe7fe7 x11xxxxxx0f2f2 111xxxx0x0v4v4 11xxxxx0xxfe8fe8 xx000xxxxxf9f9 xx000x11x1v5v5 xx0xxx11x1f e 10 xxx0xxxx1xf9f9 x0x01xxx1xv6v6 x0x01xxxxxf e 11

10. 10 Independent Fault Clustering Illustrative Example After Merging Components After Mapping IFSsAfter Mapping Essential Faults Cluster Test VectorFault Component FaultFault Component Fault 00x01x0x100xxxxx0x10f3f3 f3f3 1 0xx0xxxxxxf6f6 f6f6 x0x01xxxxxf 11 x0x01xxxxxf 11 0xxx1xxxx0f2f2 10x1xx00001xxxxxxx00f4f4 f4f4 2 10x1xxxxxxf5f5 f5f5 xxxxxxx00xf7f7 f7f7 xxx1xx0xxxf1f1 11000xx0xx11xxxxx0xxf8f8 f8f8 3 xx000xxxxxf9f9 xx0xxx11x1 f 10 xx0xxx11x1f 10 4 IFS 1 ={f 1,f 9 } IFS 2 ={f 2 }

11. 11 FC# DFs# CFs# TVs# Gates# Outputs# InputsCct 95.741263027471541193140233c2670 84.4522895342835016692250c3540 98.897529153501932307123178c5315 98.462966498156337951790700s13207.1f 96.67411335117256579772684611s15850.1f 100217 78104918s208.1f 1003270 2561572130142s3271f 1002870 7041789205172s3330f 1003380 2401685209226s3384f 99.436310043118014722217917421664s38417f 95.852347973630311741925317301464s38584f 1004764 1322342120153s4863f 99.131456346033592779228214s5378f 1006684 1383080294322s6669f 93.475647569276205597250247s9234.1f Experimental Results Benchmark Circuits

12. 12 Experimental Results Results by RM, GC, and IFC IFCGCRMROFCct Time (sec.)# TVsTime (sec.)# TVs# Comp# TVs 6.95968.0399761100106c2670 8.98839.08836578083c3540 3110334.951171491106119c5315 169243339.932483516252476s13207.1f 249144463.951694135181456s15850.1f 0.93320.009339433 s208.1f 7.026114.9769121276115s3271f 920811.012331263248277s3330f 7.977215.017310487582s3384f 20721455327.317312215187822s38417f 2590145925021016086232819s38584f 25.964924.01526075965s4863f 2312334.951301460145252s5378f 37.913560.014012864252s6669f 68.06172104.011852093202375s9234.1f

13. 13 Experimental Results Results by Iterative IFC Iterative IFCIFCCct Time (sec.)# Iterations# TVs 42.0768596c2670 26.9537583c3540 88.04486103c5315 473.122238243s13207.1f 374.951129144s15850.1f 0.01132 s208.1f 18.9826061s3271f 30.023196208s3330f 7.07172 s3384f 3775.062120145s38417f 8217.083124145s38584f 70.8834249s4863f 1096117123s5378f 175.0143035s6669f 200.934155172s9234.1f

14. 14 Experimental Results Summary of Results GC computes smaller test sets. –As much as 11.9% smaller compared to RM. –1% for c2670; 9.5% for s38584f; 11.9% for s4863f. Results by IFC are better compared to RM & GC. –Improvement over RM: 3% for s208.1f – 37.5% for s38584f –Improvement over GC: 1.4% for s3384f – 31% for s38584f –Runtime of IFC is better than that of GC. Iterative IFC improves over RM: 3% - 46.6%e.g. 35.8% for s38417f Iterative IFC improves over IFC: 1.6% - 17.2%e.g. 14.5% for s38584f

15. 15 Conclusion Static compaction based on Independent Fault Clustering (IFC) has been proposed. IFC is based on test vector decomposition. IFC has achieved an improvement of as much as 37.5% over random merging. Iterative IFC has achieved an improvement of as much as 46.6% over random merging and 17.2% over IFC.