Not Everything Is Permitted: Constrained Cartesian Abstractions for Optimal Classical Planning

Cartesian abstractions can flexibly approximate planning tasks to generate admissible heuristic functions. Constrained abstractions use state constraints, such as mutexes, to eliminate parts of the abstraction that cannot belong to solutions for the original problem. While this has been successfully applied to simple forms of abstraction, no previous work has explored how to do this for Cartesian abstractions. We introduce constrained Cartesian abstractions, which leverage state constraints in multiple ways: to prune spurious transitions and to simplify or even remove abstract states. Moreover, we also use disambiguation to better guide the counterexample-guided process used to generate the abstractions. Our experimental results show that the resulting constrained Cartesian abstractions induce more informed heuristics than their non-constrained counterpart.