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Automatic Abstraction Refinement for GSTE

Automatic Abstraction Refinement for GSTE. Yan Chen, Yujing He, and Fei Xie Portland State University Jin Yang Intel. Nov 13, 2007. Our Contributions. AutoGSTE – An automatic approach to abstraction refinement for GSTE

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Automatic Abstraction Refinement for GSTE

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  1. Automatic Abstraction Refinement for GSTE Yan Chen, Yujing He, and Fei Xie Portland State University Jin Yang Intel Nov 13, 2007

  2. Our Contributions • AutoGSTE – An automatic approach to abstraction refinement for GSTE • Quickly converge to good abstractions that enable verifications that are not possible before • Allow assertion graphs to be high-level w/o adapting too much to circuit implementation

  3. Outline • Overview of (G)STE • Quaternary Abstraction and its Imprecision • Our Solution – AutoGSTE • Counterexample-guided abstraction refinement • Model refinement and specification refinement • Experiments • Conclusion & Future Work

  4. Symbolic Trajectory Evaluation [Bryant & Seger] • Scalability • Model checking complexity largely depends on the complexity of the assertion rather than the circuit • Pros: Highly efficient • Cons: • False negatives due to insufficient input constraints • R. Tzoref, O. Grumberg, Automatic refinement and vacuity detection for STE, CAV’06 • J. Roorda, K. Clarssen, Sat-based assistance to abstraction refinement for STE, CAV’06 • Only properties over finite time  GSTE

  5. Generalized STE [Yang & Seger] • ω-regular properties represented by assertion graphs G = { (V, v0, E, ant, cons) } • Non-deterministic execution • Fixed-point computation

  6. GSTE Algorithm Algorithm: GSTE(G, post) (* initialize symbolic simulation *) 1.foreach edge ein G 2. ife is from the initial vertex 3. sim(e) := ant(e); 4. put e in EventQueue; 5. else 6. sim(e) := { }; (* perform symbolic simulation *) 7. whileEventQueue is not empty 8. get an edge e from the queue, 9. for each successor edge e’ of ebegin 10. sim(e’) := sim(e’)  post(sim(e))  ant(e’); 11. ifthere is a change in sim(e’) 12. put e’ intoEventQueue; end (* check consequence *) 13. for each edge e in G14. if!(sim(e)  cons(e)) return false; 15. return true; end.

  7. Outline • Overview of (G)STE • Quaternary Abstraction and its Imprecision • Our Solution – AutoGSTE • Counterexample-guided abstraction refinement • Model refinement and specification refinement • Experiments • Conclusion & Future Work

  8. Quaternary-Value Logic Two sides of a coin • Significantly reduce state spaces by quaternary abstraction  • Over abstractions cause false negatives  (Conflict) (Unknown) Information Partial Order Propagation of “Unknown”

  9. 0 1 1 0 1 1 X 1 X X Causes of False Negative: Quaternary State Set Unions sim(e’) := sim(e’)  post(sim(e))  ant(e’); Check whether the output is always 1 under certain inputs Abs. A Out 1 1 1 1 X B

  10. 1 0 1 0 1 1 Causes of False Negative: Existentially Quantified-Out Symbolic Variables [A=X, B=X] Out=A|B=X A Out B [A=c1, B=(!c1|c2)] Out=A|B=c1|(!c1|c2)=1 c1,c2 is existentially quantified out after every single step simulation

  11. Outline • Overview of (G)STE • Quaternary Abstraction and its Imprecision • Our Solution – AutoGSTE • Counterexample-guided abstraction refinement • Model refinement and specification refinement • Experiments • Conclusion & Future Work

  12. AutoGSTE: Automatic Abstraction Refinement Circuit Impl. Assertion Graph Abstraction refinement: (monotonic) (1) Constraining inputs with symbolic constants/variables (2) Model refinement: introducing precise nodes (3) Spec refinement: assertion graph transformations (1) GSTE Refined Abstraction (3) Abstraction Refinement Assertion holds Counter Example (2) Counter Example Analysis Causes of Imprecision Assertion fails Causes of imprecision in GSTE’s quaternary abstraction: (1) Under-constrained inputs; (2) Quaternary state set unions; (3) Existentially quantified-out symbolic variables

  13. Counter Example Analysis • Counter Example • [(edge1,src1,dest1),…,(edgeT, srcT,destT)] • Identify “X” nodes in destT that violates consequent on edgeT • Backtrack to identify the causes for “X” node N • In the end, the following causes will be identified: • Output circuit nodes/assertion edges on which Xs are introduced.

  14. AutoGSTE: Automatic Abstraction Refinement Circuit Impl. Assertion Graph Abstraction refinement: (1) Constraining inputs with symbolic constants/variables (2) Model refinement: introducing precise nodes (3) Spec refinement: assertion graph transformations (1) GSTE Refined Abstraction (3) Abstraction Refinement Assertion holds Counter Example (2) Counter Example Analysis Causes of Imprecision Assertion fails Causes of imprecision in GSTE’s quaternary abstraction: (1) Under-constrained inputs; (2) Quaternary state set unions; (3) Existentially quantified-out symbolic variables

  15. Model Refinement • Symbolic Indexing (Verifier has to encode it in the specification) Abs. Abs. rew. Partition Finer Partition rew.

  16. Model Refinement (Cont.) • Precise Nodes: Circuit nodes that must always have boolean values by symbolic indexing • [Yang and Seger, FMCAD’02] Manually specify precise nodes to eliminate Xs caused by both unions and weaks. • AutoGSTE automatically marks precise nodes • Mark all the identified nodes as precise • Mark one node at a time (control signals first?)

  17. …… Specification Refinement • Loop unrolling transformations address unions • Allow the specification to be high level • Dynamically adapt to the real computation flow of the circuit

  18. Specification Refinement (Cont.) • Automating loop unrolling • Unroll each problematic edge to prevent unwanted state set unions 2 1 3 4

  19. Specification Refinement (Cont.) • Case splitting transformations address weaks • Symbolic variables symbolically index a set of edges with scalar values • Remember the variable values by case splitting

  20. Outline • Overview of (G)STE • Quaternary Abstraction and its Imprecision • Our solution – AutoGSTE • Counterexample-guided abstraction refinement • Model Refinement .vs. Specification Refinement • Experiments • Conclusion & Future Work

  21. Experiment: FIFO

  22. FIFO Model Refinement Better than manual analysis!

  23. FIFO Specification Refinement Too complex to do manually!

  24. Conclusion & Future Work • An automatic approach to abstraction refinement for GSTE • Quickly converge to good abstractions • Future work • Identify minimal set of precise nodes • Reduce unnecessary loop-unrolling/case-splitting • Integrate model refinement and spec refinement

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