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Syntax-driven partitioning for model-checking of Esterel programs

Syntax-driven partitioning for model-checking of Esterel programs. Eric Vecchié - INRIA Tick. Introduction. Esterel Synchronous reactive structural programming (structure = sequence, parallel, if-then-else...) circuit translation (gates+registers) Objective

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Syntax-driven partitioning for model-checking of Esterel programs

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  1. Syntax-driven partitioning for model-checking of Esterel programs Eric Vecchié - INRIA Tick

  2. Introduction • Esterel • Synchronous reactivestructural programming (structure = sequence, parallel, if-then-else...) • circuit translation (gates+registers) • Objective • Efficient Reachable State Space computation • Contribution • Rely on program structural syntax to reduce the size of intermediate computations

  3. The Wristwatch example TIME_SET DISPLAY ALARM_SET STOPWATCH

  4. RSS : Breadth-First Search P abort P when S; present T then Q1 else Q2 end; R Q2 Q1 R

  5. Partitioning - overview Q1 P S R Q2

  6. Partitioning - detail

  7. Sequence / if-then-else S S P1 P1 P2 S P2 P3 Q

  8. Parallel and signals || P1 Q1 R1 S1 P2 Q2 S2 Q3 R2

  9. How to partition ? • Partition register structure according to program blocks • Frontiers synthesized from signal receptions present statements abort statements Only enlarging (removing frontiers)but applying to pending states past "last" frontier • Generated from control flow graph

  10. Symbolic methods Binary Decision Diagrams (BDDs) allow to represent : • Boolean functions • Sets (in a finite universe) • Partitioned Transition Relations (according to individual target registers)

  11. Cofactoring Given a domain D, reduce the BDD of a function f: f↑D(x) = f(x) if x belongs to D Reduces individual transition functions relative to source domain

  12. Control Flow Graph construction abort loop pause end ; present T then pause ; pause pause pause || || when S else pause end

  13. Problem on loops P Q

  14. Conclusion • Program verification following program syntax • Sequences, if-then-else • Signals in parallels • Less memory required • Smaller intermediate BDDs • Lighter transition relation • Lighter image computation

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