Existence of an exponential-time algorithm for IFO verification

Determine whether there exists an algorithm that decides initial-and-final-state opacity (IFO) for discrete-event systems modeled by nondeterministic finite automata with partial observation in worst-case exponential time O^*(2^n), rather than the currently known super-exponential upper bound O^*(2^{n^2}).

Background

Initial-and-final-state opacity (IFO) asks whether an observer can deduce that a computation started in a given initial state and ended in a given final state, given limited observations. Two main verification approaches have been studied: a trellis-based semigroup construction and a reduction to language inclusion (observer-based). For both, known worst-case bounds are super-exponential O^*(2^{n^2}).

Under SETH-based lower bounds, subexponential improvements are ruled out, but these do not exclude an exponential-time algorithm. The paper proves tightness of the super-exponential bounds for the two textbook algorithms, while leaving the existence of an exponential-time algorithm open.