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Advancements in Partitioning Methodology for BDD-based Verification Techniques

This paper presents a novel partitioning methodology aimed at improving BDD-based verification processes, particularly in reachability analysis. The study addresses key challenges in partitioned reachability, exploring fundamental questions regarding when, how, and what to partition. Through experimental results on VIS benchmarks, the methodology's effectiveness is showcased, demonstrating the potential of Partitioned OBDD (POBDD) to enhance efficiency in various reachability problems. The findings advocate for trace-centric approaches and reveal the need for dynamic partitioning strategies for optimal performance.

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Advancements in Partitioning Methodology for BDD-based Verification Techniques

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  1. A Partitioning Methodology for BDD-based Verification D. Sahoo, Stanford S. Iyer, UT-Austin J. Jain, Fujitsu C. Stangier, Fujitsu A. Narayan, BDA D. Dill, Stanford E. A. Emerson, UT-Austin IWLS 2004

  2. Outline • Background • The Partitioning Methodology • Experimental Results • Conclusion

  3. Motivation • BDD-based Verification • Reachability Analysis • Partitioned Reachability Analysis • Problems of Partitioned-based Reachability

  4. What Are Partitioned OBDDs? For FV, replace BDDs by POBDDs (Jain 92) x1 X3 = 0 X3 = 1 x2 x2 x1 x1 x2 x2 x2 x3 x4 x4 x4 x4 0 1 x4 0 1 0 1

  5. w2 w1 I1(x) I3(x) w3 w4 Event Queue 1 3 Reachability using Partitioned-ROBDDs

  6. w2 w1 I1(x) T11 I3(x) w3 w4 Event Queue 3 Reachability using Partitioned-ROBDDs

  7. Event Queue 3 4 Reachability using Partitioned-ROBDDs w2 w1 T12 R1 T14 T13 I3(x) w3 w4

  8. w2 w1 R1 T33 I3(x) w3 w4 Event Queue 4 Reachability using Partitioned-ROBDDs

  9. w2 w1 R1 T31 T32 T34 R3 w3 w4 Event Queue 4 2 1 Reachability using Partitioned-ROBDDs

  10. w2 w1 R1 T44 R3 w3 w4 Event Queue 1 2 Reachability using Partitioned-ROBDDs

  11. Challengesin POBDD-based Verification Creating Partitions: 6 Basic Questions • When to partition? • How to partition? • How many partitions? • What type of partitions? • Where to re-partition? • How to process partitions?

  12. New Partitioning Methodology • Initial Partitioning • Choice of Partitioning Variable • Global Dynamic Partitioning • Local Partitioning • Scheduling • Trace-based decisions

  13. Initial Partitioning • Easy Reachability • Leads to a better Partitioning Strategy

  14. Choice of Partitioning Variable • Cost function • Trace-based selection

  15. Choice of Partitioning Variable • Cost function • Trace-based selection

  16. Global Dynamic Partitioning • Blowup in a Partition • Balanced Partitioning Strategy

  17. Local Partitioning • Non-compatible Intermediate functions Memory

  18. Scheduling • Partition Traversal order • Cost function • Density based scheduling • Time based scheduling

  19. Trace-based decisions • Try different configurations • Pick the best ?

  20. Results on VIS Benchmarks (All circuits reported where VIS needs > 250K BDD nodes) T = Timeout, M/O = Memout

  21. Comparisons

  22. Summary • Proved viability of POBDDs by answering fundamental questions on partitioning • What/when/how/where/… to partition • POBDDs can be more efficient for many reachability problems but somewhat unstable • Requires trace-centric approach • Preliminary results shown.

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