Transition Landmarks from Abstraction Cuts

We introduce transition-counting constraints as a principled tool to formalize constraints that must hold in every solution of a transition system. We then show how to obtain transition landmark constraints from abstraction cuts. Transition landmarks dominate operator landmarks in theory but require solving a linear program that is prohibitively large in practice. We compare different constraints that project away transition-counting variables and then further relax the constraint. For one important special case, we provide a lossless projection. We finally discuss efficient data structures to derive cuts from abstractions and store them in a way that avoids repeated computation in every state. We compare the resulting heuristics both theoretically and on benchmarks from the international planning competition.