In the previous sections we have constructed a semantics for PDDL+ by mapping to Hybrid Automata and we have constructed a formal relationship between plans and traces. As a consequence, we can demonstrate that in general PDDL+ domains provide succinct encodings of their corresponding Hybrid Automata, since a PDDL+ model can have a state space that is exponential in the size of the encoding.
Having established the relationship between PDDL+ domains and Hybrid Automata, we can now benefit from the large body of research into Hybrid Automata and their sub-classes. One issue that has been widely addressed is the boundary between decidable and undecidable classes of Hybrid Automata and this boundary can be reinterpreted for the reachability question for interesting subsets of the PDDL+ language.
In the following we only consider subsets of PDDL+ that are interesting in the sense of modelling different kinds of restricted continuous temporal behaviours.