Domain-independent optimal planning has seen important breakthroughs in recent years with the development of tractable and informative admissible heuristics, suitable for planners based on forward state-space search. These heuristics allow planners to optimally solve an important number of benchmark problems, including problems that are quite involved and difficult for the layman. In this paper we present a new admissible heuristic that is obtained from the state equation associated to the Petri-net representation of the planning problem. The new heuristic, that does not fall into one of the four standard classes, can be computed in polynomial time and is competitive with the current state of the art for optimal planning, as empirically demonstrated over a large number of problems, mainly because it often shows an improved quality-to-cost ratio. The new heuristic applies to SAS+ planning tasks with arbitrary non-negative action costs.

We study the relationship between optimal planning algorithms, in the form of (iterative deepening) A* with (forward) state-space search, and the reduction of the problem to SAT. Our results establish a strict dominance relation between the two approaches: any iterative deepening A* search can be efficiently simulated in the SAT framework, assuming that the heuristic has been encoded in the SAT problem, but the opposite is not possible as A* and IDA* searches sometimes take exponentially longer.