A Kantorovich-Monadic Powerdomain for Information Hiding, with Probability and Nondeterminism

We propose a novel domain-theoretic model for nondeterminism, probability and hidden state, with relations on it that compare information flow. One relation is Smyth-like, based on a structural, refinement-like order between semantic elements; the other is a testing order that generalises several extant entropy-based techniques. Our principal theorem is that the two orders are equivalent. The model is based on the Giry/Kantorovich monads, and it abstracts Partially Observable Markov Decision Processes by discarding observables´ actual values but retaining the effect they had on an observer´s knowledge. We illustrate the model, and its orders, on some small examples, where we find that our formalism provides the apparatus for comparing systems in terms of the information they leak.