Tightness of the upper-bound time complexity for the general inclusion-based IFO verification (Algorithm 3)

Establish whether the theoretical upper-bound time complexity O^*(2^{n^2}) of the general inclusion-based IFO verification algorithm (Algorithm 3), which reduces IFO to language inclusion using subset/observer-based techniques, is tight by proving a matching worst-case lower bound or refuting it.

Background

Algorithm 3 encapsulates inclusion-based verification approaches that reduce IFO to language inclusion and rely on observer/subset constructions. Its theoretical upper bound matches the super-exponential bound of the trellis-based and classical observer-based algorithms.

While the paper shows tightness for the two textbook algorithms, it does not establish tightness for Algorithm 3, leaving open whether instances force the same super-exponential behavior or whether better worst-case complexity is achievable.