Maximality of the eager-rule fragment

Determine whether the qualitative timeline-based planning fragment defined by eager rules is maximal among rule fragments that permit recognition of solution plans by deterministic finite automata of singly exponential size; specifically, ascertain whether any strictly larger set of synchronization rules beyond the eager rules still supports the direct construction of such deterministic automata for plan existence and strategy synthesis.

Background

The paper introduces the eager-rule fragment of qualitative timeline-based planning, which restricts synchronization rules so that solution plans can be recognized by deterministic finite automata (DFAs) of singly exponential size. This avoids the exponential blowup from determinizing nondeterministic automata and enables an EXPTIME procedure for strategy synthesis.

The authors prove that these eager-rule restrictions are sufficient to build such DFAs and also identify a maximal subset of Allen’s interval relations that fits within this fragment. However, they do not establish that the fragment itself is maximal with respect to the determinization-friendly property, leaving open whether broader classes of synchronization rules could still admit the same DFA-based approach.