Identifiability over implicitly specified hypothesis classes

Determine identifiability within an implicitly specified hypothesis class, rather than only for a stated pair of candidate Regular Decision Processes.

Background

The paper develops PEC for deciding policy-relative observational equivalence between two explicitly given Regular Decision Processes and emphasizes that this pairwise setting differs from deciding identifiability over an implicitly specified hypothesis class. Such a class could contain many possible automaton structures rather than a fixed pair selected in advance.

The authors identify extending the analysis to implicitly specified hypothesis classes as outside the scope of the presented decision procedure. The problem is unresolved because PEC takes a known candidate pair as input and does not provide a general procedure for determining whether data identify a model within a broader, implicitly defined class.