Minimizing Counterexample with Refutation Analysis and Incremental SAT

1. Minimizing Counterexample with Refutation Analysis and Incremental SAT Shengyu Shen School of Computer Science National University of Defence Technology

2. Outline • Motivation • Brute Force Lifting algorithm • Refutation Analysis • Experiment Result • Conclusion

3. Motivation • Model Checker generate counterexample to explain property violation. • Long counterexample of complex system are very hard to be understand.

4. Example • DiVer can search 96 steps for a circuit with 416k gates and 12.7k latches • Pankaj Chauhan’s symbolic simulator can search 183 steps for a circuit with 4494 latches.

5. Outline • Motivation • Brute Force Lifting algorithm • Refutation Analysis • Experiment Result • Conclusion

6. Free W0 W1 W2 Property violation X0 X1 X2 X3 BFL Concept CEX : Free  {0,1}

7. W0 W1 W2 X0 X1 X2 X3 BFL Concept(Cont. 1) 0 1 Property violation Property violation again Thus W2 is an irrelevant variable

8. BFL Concept(Cont. 2) • Thus variable v is irrelevant  • Λ0ik-1T(Si,Si+1) fkAssign(Free-{v}) is UNSAT

9. Try W2 Try W1 Try W0 W0 W1 W2 X0 X1 X2 X3 Try X0 BFL Implementation

10. BFL—Difficulty and Solution • Difficulty: Too high run time complexity Why: Need to call SAT solver for very free variables Solution: Reduce the number of calling SAT solver How: Eliminate multiple variables after every SAT solving

11. Outline • Motivation • Brute Force Lifting algorithm • Refutation Analysis • Experiment Result • Conclusion

12. The set of Unit Clause S All literal of c Refutation Analysis If {v} or {v} S, then v R When UNSAT There must be a conflict clause c at decision level 0

13. Try W2 R W0 W1 W2 X0 X1 X2 X3 BFL with Refutation Analysis Property violation

14. Outline • Motivation • Brute Force Lifting algorithm • Refutation Analysis • Experiment Result • Conclusion

15. 1st step of our approach BFL 2nd step of our approach Experiment Result |Free| time

16. Conclusion • Our approach is 1~2 order of magnitude faster than BFL. • Our approach achieve this speedup with only minor lost in its counterexample minimization ability.