Local and Symbolic Bisimulation Using Tabled Constraint Logic Programming

Bisimulation is a fundamental notion that characterizes behavioral equivalence of concurrent systems. In this paper, we study the problem of encoding eÆcient bisimulation checkers for niteas well as in nite-state systems as logic programs. We begin with a straightforward and short (less than 10 lines) encoding of nite-state bisimulation checker as a tabled logic program. In a goal-directed system like XSB, this encoding yields a local bisimulation checker: one where state space exploration is done only until a dissimilarity is revealed. Local checking can often outperform the traditional global checking by several orders of magnitude even for nite-state systems, as our experimental results show. Surprisingly, even when the systems are equivalent where the entire state space may need to be explored, the performance of our local checker is comparable to hand-coded equivalence checking algorithms implemented in other veri cation tools. More importantly, the logic programming formulation of local bisimulation can be extended to do symbolic bisimulation for checking the equivalence of in nite-state concurrent systems represented by symbolic transition systems. We show how the two variants of symbolic bisimulation (late and early equivalences) can be formulated as a tabled constraint logic program in a way that precisely brings out their di erences. We use a a constraint meta-interpreter over disequality constraints that evaluates tabled constraint logic programs to support the symbolic bisimulation checker. We present experimental results to illustrate the practical eÆcacy of our logic programming based symbolic bisimulation checker. Finally, we show that our symbolic bisimulation checker, despite the overheads imposed by the constraint meta-interpreter, actually outperforms non-symbolic checkers even for relatively small nite-state systems. This research was partially supported by NSF Grants CDA-9805735, EIA-9705998, CCR-9876242, and CCR 9732186.