Optimal Metric Planning with State Sets in Automata Representation

This paper proposes an optimal approach to infinite-state action planning exploiting automata theory. State sets and actions are characterized by Presburger formulas and represented using minimized finite state machines. The exploration that contributes to the planning via model checking paradigm applies symbolic images in order to compute the deterministic finite automaton for the sets of successors. A large fraction of metric planning problems can be translated into Presburger arithmetic, while derived predicates are simply compiled away. We further propose three algorithms for computing optimal plans; one for uniform action costs, one for the additive cost model, and one for linear plan metrics. Furthermore, an extension for infinite state sets is discussed.