Heuristics for Hierarchical Partitioning with Applications to Model Checking

Oliver Moller and Rajeev Alur

Given a collection of connected components, it is often desired to cluster together parts of strong correspondence, yielding a hierarchical structure. We address the automation of this process and apply heuristics to battle the combinatorial and computational complexity.

We define a cost function that captures the quality of a structure relative to the connections and favors shallow structures with a low degree of branching. Finding a structure with minimal cost is NP-complete. We present a greedy polynomial-time algorithm that creates an approximative good solution incrementally by local evaluation of a heuristic function. We argue for a heuristic function based on four criteria: the number of enclosed connections, the number of components, the number of touched connections and the depth of the structure.

We report on an application in the context of formal verification, where our algorithm serves as a preprocessor for a temporal scaling technique, called ``Next'' heuristic. The latter is applicable in reachability analysis and is included in a recent version of the Mocha model checking tool. We demonstrate performance and benefits of our method and use an asynchronous parity computer and an opinion-poll protocol as case studies.

11th Advanced Research Working Conference on Correct Hardware Design and Verification Methods (CHARME'01), 2001.