Least fixpoint approximations for reachability analysis

The knowledge of the reachable states of a sequential circuit can dramatically speed up optimization and model checking. However, since exact reachability analysis may be intractable, approximate techniques are often preferable. H. Cho et al. (1996) presented the machine-by-machine (MBM) and frame-by-frame (FBF) methods to perform approximate finite state machine (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 show that there exists a class of methods-least fixpoint approximations-that compute the same results as RFBF ("reached FBF", one of the FBF methods). We show that one member of this class, which we call "least fixpoint MBM" (LMBM), is as efficient as MBM, but provably more accurate. Therefore, the trade-off that existed between MBM and RFBF has been eliminated. LMBM can compute RFBF-quality approximations for all the large ISCAS-89 benchmark circuits in a total of less than 9000 seconds.