Least Fixpoint MBM: Improved Technique for Approximate Reachability

Reachability don’t cares (RDCs) can have a dramatic impact on sequential optimization and CTL model checking. However, since the computation of RDCs is often intractable, approximate reachability don’t cares (ARDCs) are often preferable. The challenge in computing approximations of the reachable states is to obtain the best accuracy within given time and memory limits. Cho et al. presented the Machine-By-Machine (MBM) and Frame-ByFrame (FBF) methods to perform approximate FSM traversal. FBF produces tighter upper bounds than MBM; however, it usually takes much more time and it may have convergence problems. In this paper, we present a new method that produces the same upper bounds as RFBF (Reached FBF, one of the FBF methods), and is as fast and efficient as MBM, but more accurate. Since the original MBM is a greatest fixpoint computation and the new method is a least fixpoint MBM, we call the new method LMBM (Least fixpoint MBM).

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