Practical CNF Interpolants Via BDDs

Craig interpolation has been recently shown to be useful in a wide variety of problem domains. One use is in strategy extraction for two player games, as described in our accompanying submission. However, interpolation is not without its drawbacks. It is well-known that an interpolant may be very large and highly redundant. Subsequent use of the interpolant requires that it is transformed to CNF or DNF, which will further increase its size.

We present a new approach to handling both the size of interpolants and transformation to clausal representation. Our approach relies on the observation that in many real-world applications, interpolants are defined over a relatively small set of variables. Additionally, in most cases there likely exists a compact representation of the interpolant in CNF. For instance, in our application to games an interpolant represents a set of winning states that is likely to have a simple structure.