Homomorphisms and Embeddings of STRIPS Planning Models

Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance $P$ and a sub-instance of another instance $P^{\prime }$. One application of such a mapping is to efficiently produce a compiled form containing all solutions to $P$ from a compiled form containing all solutions to $P^{\prime }$. We also introduce the notion of embedding from an instance $P$ to another instance $P^{\prime }$, which allows us to deduce that $P^{\prime }$ has no solution-plan if $P$ is unsolvable. In this paper, we study the complexity of these problems. We show that the first is GI-complete and can thus be solved, in theory, in quasi-polynomial time. While we prove the remaining problems to be NP-complete, we propose an algorithm to build an isomorphism when possible. We report extensive experimental trials on benchmark problems that demonstrate conclusively that applying constraint propagation in preprocessing can greatly improve the efficiency of a SAT solver.