1. Verifying Dijktra’s algorithm in Jahob
Jonathan Kuhn
Robin Mange
EPFL-SSC

2. Our goals Acquire practical skills in software verification
Statement checking through implementation
Performance evaluation
Discussion

3. Reminder: Dijkstra’s algorithm
Computes shortest-paths in directed graphs
No negative weight edges
Widely used in networking in routing protocols (e.g. OSPF)

4. Implementation Class Node {} Class Path {} Class Vector{}
Class Integer{}
Class Dijkstra{}
Simulated classes for Vector and Integer Objects

5. Implementation Init Fill up Vector 1 Main loop of the algorithm
While vector 1 is not empty, take the node corresponding to the smallest distance. Remove it from vector 1, and recompute all edges to update minimal distances
Fill up Vector 1
Add to the vector 1 all the node except the starting one
Init
Set distances to -1 and 0 for the start node. Set empty arrays for previous (node)
Distances and previous arrays have to be initialized
Vector 1 needs to be initialized
Specifications of above need to be maintained.

6. Verification:
Unfortunately We still have a method that is not verified.
We already can say that:
The execution time of a verification process of our entire program (~200 lines) is about 20min…
The number of annotation lines is about 80 for 200 lines of code.

7. Performance VC generation algorithms can be exponential in code size
Can lead to long verification times (even for small programs)
Important to write modularized code
ESC/Java is known to be faster… but has more drawbacks than Jahob
E.g. no infinite loop check, arithmetic overflow, unsound, …

8. Discussion Problems encountered
Jahob doesn’t support libraries: need to simulate them
Int and objects aren’t treated the same way in decision procedures
Strange behavior with invariants in rare cases

9. But…
Jahob was mostly tested on small data structures (linked lists, …)
Can be enhanced and extended beyond current state
Very promising!

10. Related work
To do: To test several benchmarks to test the correctness of the verification process.
If time allows: Use ESC/Java to compare performances with Jahob Translating annotations would be straightforward .