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A New Reachability Algorithm for Symmetric Multi-processor Architecture

A New Reachability Algorithm for Symmetric Multi-processor Architecture. D. Sahoo, Stanford J. Jain, Fujitsu S. Iyer, UT-Austin D. Dill, Stanford. PDMC 2005. Reachability using BDD. [Burch et al. : 91]. Partitioned Transition Relation. Initial State. I. …. …. R 1. Image computation.

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A New Reachability Algorithm for Symmetric Multi-processor Architecture

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  1. A New Reachability Algorithm for Symmetric Multi-processor Architecture D. Sahoo, Stanford J. Jain, Fujitsu S. Iyer, UT-Austin D. Dill, Stanford PDMC 2005

  2. Reachability using BDD [Burch et al. : 91] Partitioned Transition Relation Initial State I … … R1 Image computation Trn Tri Tr1 R2 Least Fixed Point Ri

  3. Local Fixed Point 1 Local Fixed Point 2 Local Fixed Point 3 Local Fixed Point 4 Partitioned Reachability using POBDD POBDD - [Jain : 92] Reachability - [Narayan et al. : 97] I Initial States : I

  4. Local Fixed Point 3 Local Fixed Point 4 Communicate from 1 -> 2 Communicate from 1 -> 4 Communicate from 1 -> 3 Partitioned Reachability using POBDD POBDD - [Jain : 92] Reachability - [Narayan et al. : 97] I Initial States : I Local Fixed Point 1 Local Fixed Point 2

  5. Local Fixed Point 1 Local Fixed Point 2 Local Fixed Point 3 Local Fixed Point 4 Communicate from 2 -> 1 Communicate from 2 -> 3 Communicate from 2 -> 4 Partitioned Reachability using POBDD POBDD - [Jain : 92] Reachability - [Narayan et al. : 97] I Initial States : I Similarly repeat for other partitions

  6. Local Fixed Point 1 Local Fixed Point 2 Local Fixed Point 3 Local Fixed Point 4 Partitioned Reachability using POBDD POBDD - [Jain : 92] Reachability - [Narayan et al. : 97] I Improvements: [Iyer et al. : 03] [Sahoo et al. : 04]

  7. Motivation for Multi-threaded Approach • Scheduling Problem • Increasing availability of powerful SMP machines • Multi-threading is a way of achieving real parallelism in SMP machines

  8. Multi-threaded Reachability [DAC 05] Naïve parallelization Time • Advantage: • Parallel speedup • Catch a bug faster than the sequential version • Problems: • Not much parallelism

  9. Multi-threaded Reachability [DAC 05] Early Communication Time • Advantage: • Parallel speedup • Finishes the reachability analysis faster • Catches bug faster than the naive version • Problems: • Parallelism could be better

  10. Multi-threaded Reachability [DAC 05] Early Communication and Partial Communication Time • Advantage: • Parallel speedup • Finishes the reachability analysis faster • Catches bug faster than the previous versions

  11. Reachability in SMP Architecture Time • We find the bugs faster ! • Improved parallelism • Better parallel speedup

  12. Results on Industrial Circuits

  13. Results on public benchmarks

  14. Performance : Non-deterministic Vs Deterministic

  15. Results : Gantt charts Real execution traces from our multi-threaded reachability program

  16. Conclusion and Future Work • Parallelize the Reachability • Multi-threaded Reachability • Better results • Deterministic behavior • Future Work • Improve the parallelism further • Study cache behavior

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