Exact Distinguishability in Non-Markovian Decision Processes
This study addresses the challenge that the distinguishability assumptions underlying offline guarantees in non-Markovian decision processes are difficult to verify and prone to failure. Drawing upon finite automata theory and Bayesian inference, we prove the posterior odds invariance of observationally equivalent models, thereby providing the first precise characterization of indistinguishability. Based on this theoretical foundation, we propose PEC, a linear-time decision algorithm, and formally verify its core theorems using Lean 4. Experimental results demonstrate that conventional assumptions frequently fail in practice, whereas the PEC algorithm effectively restores distinguishability, ensuring that the theoretical guarantees for offline policy evaluation remain valid.