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

2. Introduction Esterel –Synchronous reactive structural 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 ALARM_SET TIME_SET STOPWATCH DISPLAY

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

5. P Partitioning - overview Q1 Q2 R S

6. Partitioning - detail

7. Sequence / if-then-else P1P1 P2P2 P3P3 P1P1 P2P2 Q S S S

8. Parallel and signals || P1P1 Q1Q1 R1R1 P2P2 Q2Q2 Q3Q3 R2R2 S1 S2

9. How to partition ? 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 Partition register structure according to program blocks

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

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

13. Problem on loops P Q

18. 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