Efficient BDD Encodings for Partial Order Constraints with Application to Expert Systems in Software Verification

We introduce a class of computational problems called the partial order constraint satisfaction problems (POCSPs) and present three methods for encoding them as binary decision diagrams (BDDs). The first method, which simply augments domain constraints with the transitivity and asymmetry for partial orders, is improved by the second method, which introduces the notion of domain variables to reduce the number of Boolean variables. The third method turns out to be most useful for monotonic domain constraints, because it requires no explicit encoding for the transitivity. We show how those methods are successfully applied to expert systems in a software verification domain.