Efficient Reachability Analysis for Verification of Asynchronous Systems

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Efficient Reachability Analysis for Verification of Asynchronous Systems Nishant Sinha

Outline 2

Formal Verification: Introduction 3

Model Checking . . K 2 K 4

Asynchronous Systems Symbolic Reduced State-Space 5

Symbolic Model Checking t 3 t 1 N(a, a’) = s 1 s 0 a < a’ t 2 s 0 s 1 a 0 0 0 1 1 a 0 a’ a’ 0 1 1 1 a’ 1 1 6

Partial-Order Reduction s 0’ a b b a s 1’ 7

Reachability Analysis 8

The Bigger Picture I 1 I 2 Combinational Circuit Delay o 1 o 2 o 1 = 0 o 2 = 0 o 1 = 1 o 2 = 1 o 1 = 0 o 2 = 1 ? 9

Symbolic Reachability : Image Computation 10

Illustration: Intermediate BDD Sizes Dining Philosophers model Iterations 11

Partitioned Transition Relations N 1 N 2 N 3 [BCL 91] J. R. Burch, E. M. Clarke, and D. E. Long. Symbolic model checking with partitioned transition relations. In A. Halaas and P. B. Denyer, editors, International Conference on Very Large Scale Integration, pages 49 -58, Edinburgh, Scotland, 1991. North-Holland. 12

BDD blowup [BCL 91] J. R. Burch, E. M. Clarke, and D. E. Long. Symbolic model checking with partitioned transition relations. In A. Halaas and P. B. Denyer, editors, International Conference on Very Large Scale Integration, pages 49 -58, Edinburgh, Scotland, 1991. North-Holland. 13

Modified Breadth-First Search (MBFS) N 1* N 2* N 3* 14

Illustration: BDD Blowup in MBFS N 2 s 0 N 1 s 2 (10) N 1, N 2 0 v 1 MBFS N 1 0 s = (v 2, v 1, . . . ) N 1, N 2, N 3, . . . s 3 (01) v 2 . . . (11) (00) v 2 N 3 s 1 v 2 MBFS N 2 0 N 3 1 v 1 0 BDD explosion MBFS 1 1 1 (s 0) (s 0, s 2) 1 (s 0, s 1, s 2) N 1 1 (s 0, s 1, s 2, s 3) 15