We present a new abstraction refinement algorithm to better refine the abstract model for formal property verification. In previous work, refinements are selected either based on a set of counter examples of the current abstract model, as in [5, 6, 7, 8, 9, 20, 21], or independent of any counter examples, as in [18]. We (1) introduce a new controllability analysis that is independent of any particular counter examples, (2) apply a new cooperativeness analysis that extracts information from a particular set of counter examples and (3) combine both to better refine the abstract model. We implemented the algorithm and applied it to verify several real-world designs and properties. We compared the algorithm against the abstraction refinement algorithms in [20] and [21] and the interpolation-based reachability analysis in [15]. The experimental results indicate that the new algorithm outperforms the other three algorithms in terms of runtime, abstraction efficiency (as defined in [20]) and the number of proven properties.
From Many Places to Few: Automatic Abstraction Refinement for Petri Nets