On the Relation between Star-Topology Decoupling and Petri Net Unfolding
Petri net unfolding expands concurrent sub-threads of a transition system separately. In AI Planning, star-topology decoupling (STD) finds a partitioning of state variables into components whose dependencies take a star shape, and expands leafcomponent state spaces separately. Thus both techniques rely on the separate expansion of state-space composites. How do they relate? We show that, provided compatible search orderings, STD state space size dominates that of unfolding if every component contains a single state variable, and unfolding dominates STD in the absence of prevail conditions (nondeleted action preconditions). In all other cases, exponential state space size advantages are possible on either side. Thus the sources of exponential advantages of STD are exactly a) state space size in the presence of prevail conditions (our results), and b) decidability of reachability in time linear in state space size vs. NP-hard for unfolding (known results).