PAT: Towards Flexible Verification under Fairness

1. PAT: Towards Flexible Verification under Fairness http://pat.comp.nus.edu.sg Jun Sun, Yang Liu, Jin Song Dong, Jun Pang

2. Fairness is Necessary • Bounded by-pass, Peterson’s mutual exclusion protocol • weak fairness • <>[] one-leader, self-stabilizing leader election in complete networks [Fischer et al 2006] or rooted trees [Canepa et al 2008] • weak fairness • <>[] one-token, token circulation [Angluin et al 2005] or leader election [Fischer et al] in network rings • Strong global fairness

3. Weak Fairness • A process/event must be executed if always enabled.

4. Strong Fairness • A process/event must be executed if repeatedly enabled.

5. Strong Global Fairness • If a step is infinitely often enabled, it must be taken infinitely.

6. The Algorithm • Automata-based LTL model checking • weak fairness: SCC search • strong fairness: strongly connected sub-graph search • strong global fairness = terminal SCC search

7. How to Apply Fairness • One notion of fairness for the whole system • Pro: no additional user inputs. • Con: sometimes overwhelming; partial order reduction is applicable to weak fairness. • Associate individual events with different fairness • Pro: feasibility; partial order reduction • Con: user expertise required

8. Experiment Results

9. Fairness and Abstraction • Model checking parameterized systems • network protocols are often designed for arbitrary or even unbounded number of nodes. • process identify and process counter abstraction • under fairness? • Model checking real-time systems • Time abstraction • under fairness?

10. PAT Architecture