Leaping Loops in the Presence of Abstraction

1. Leaping Loops in the Presence of Abstraction • Thomas Ball • Orna Kupferman • Mooly SagivPresentation by Erkan Keremoglu

2. Motivation • Abstraction is widely used in software verification • Techniques using abstraction lose precision in the presence of loops • Refinement methods will generate a predicate for each iteration • This approach analyzes termination of loops without refinemets

4. The Idea • Replace may transitions by must transitions • This is done by checking conditions that guarentee that the transitions of the concrete system builds an acyclic connected graph • Finiteness of the concrete states guarenteed the finiteness of the graph

5. Transitions • mayand must transitions • may transitions are not transitive --> may (a, a'), may (a',a'') but still for all c in a and c'' in a'' we may not have a transition from c to c''

6. Leaping Loops • Two theorems are checked to decide termination of loops • This theorem rules out unreachable cycles and nondeterminism inside state a

7. Example for Theorem 1 • We can conclude that there is a must path from x=0 to 3n <= x

8. Theorem 2 • This is the second theorem, this time for forward traversal • Any of the two theorems can be used for detection of termination

9. How to Implement? • The idea is to check if there are must relations between given two abstract states • If the system behaves deterministically this is easy to check in the absence of loops • The method enters the picture in cases 1 < i < n such that ai is associated with a loop • Entry and exit points are detected and either theorem 1 or 2 is checked for satisfiability

10. Calculation of Ports Using Theorem Prover • Entry and exit ports are determined by using WP and SP relations