The Myhill-Nerode Theorem for Bounded Interaction: Canonical Abstractions via Agent-Bounded Indistinguishability

ArXi:2603.21399v1 Announce Type: new Any capacity-limited observer induces a canonical quotient on its environment: two situations that no bounded agent can distinguish are, for that agent, the same. We formalise this for finite POMDPs. A fixed probe family of finite-state controllers induces a closed-loop Wasserstein pseudometric on observation histories and a probe-exact quotient merging histories that no controller in the family can distinguish. The quotient is canonical, minimal, and unique-a bounded-interaction analogue of the Myhill-Nerode theorem.