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Predictive Reachability Using a Sample-based Approach

This paper presents a novel approach to predictive reachability analysis, emphasizing its implementation through sample-based techniques. It reviews traditional methods such as monolithic and partitioned reachability, highlighting their efficiencies using Binary Decision Diagrams (BDDs). The study explores the characterization of sample computations to determine optimal reachability methods by combining forward and backward analyses. This method enhances verification speed and accuracy by minimizing the steps to a fix-point and facilitating quick error detection. Future work will focus on integrating various partitioning strategies and transition relation clustering for improved efficiency.

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Predictive Reachability Using a Sample-based Approach

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  1. Predictive Reachability Using a Sample-based Approach D. Sahoo, Stanford J. Jain, Fujitsu S. Iyer, UT-Austin D. Dill, Stanford E. A. Emerson, UT-Austin IWLS 2005

  2. Outline • BDD-based Verification • Reachability Techniques • Predictive Reachability • Results • Conclusion and Future work

  3. BDD-based Verification • BDD : • Binary Decision Diagram • Used to represent Boolean functions • Reachability Analysis • Finds bug • Finds a counter example for the invariant • Proves invariant • Efficient CTL model checking

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

  5. 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

  6. 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

  7. 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

  8. 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]

  9. Forward Invariant Check • Monolithic Reachability • Starts with the initial states • Computes Fixed point of Image Computation • Checks if all the reachable states satisfy the invariants • Partitioned Reachability • Starts with the initial states • Creates Partitions • Computes Fixed point inside each partitions • Communicate results to other partitions • Finishes if there is no new state found • Checks if all the reachable states satisfy the invariants

  10. Backward Invariant Check • Monolithic Reachability • Starts with error states • Computes Fixed point of Image Computation • Check if any of the initial state is reached • Partitioned Reachability • Starts with error states • Creates Partitions of the error states • Computes Fixed point inside each partitions • Communicate results to other partitions • Finishes if there is no new state found • Checks if any of the initial state is reached

  11. Which method is better? • We don’t know a priori • Forward Monolithic Reachability • Backward Monolithic Reachability • Forward Partitioned Reachability • Backward Partitioned Reachability • How do we take advantage of the efficiency of each method? • Look at initial few steps of the Image Computation • A sample computation • Characterize the sample computations

  12. Reachability – A sample-based Approach • Compute sample image computations for each method • Characterize the sample computations • Select a method that is more effective • Augment selected method with the states covered by the sample computations • Complete reachability steps for the selected method

  13. Characterization of the Samples • Number of Image Computation performed • Until a predefined BDD size cutoff exceeded • Total number of states covered • Total time taken during the sample computation

  14. Monolithic sample E’ I’ E I Partitioned sample Fixpt R I E Augmentation • Augment forward reachable states using both monolithic and partitioned reachability • Augment backward reachable states • Advantages: • The number of steps to reach fix-point can be reduced • Leads to fast verification • Intersection of forward and backward reachable states: • Leads to fast errors detection

  15. Results on public benchmarks

  16. Number of Timeouts Timeout of 1 day 0

  17. Conclusion and Future Work • Sample-based approach • combines Forward and backward Reachability • combines Monolithic and Partitioned Reachability • Intersection of Forward and Backward frontiers • For fast error detection • Augmentation: • Reduced number of steps to reach a Fix-point • For fast verification • Future work: • Combine different efficient partitioning strategies • Combine different Transition Relation clustering

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