Paper
The Myhill-Nerode Theorem for Bounded Interaction: Canonical Abstractions via Agent-Bounded Indistinguishability
Authors
Anthony T. Nixon
Abstract
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. For clock-aware probes, it is exactly decision-sufficient for objectives that depend only on the agent's observations and actions; for latent-state rewards, we use an observation-Lipschitz approximation bound. The main theorem object is the clock-aware quotient; scalable deterministic-stationary experiments study a tractable coarsening with gap measured on small exact cases and explored empirically at larger scale. We validate theorem-level claims on Tiger and GridWorld. We also report operational case studies on Tiger, GridWorld, and RockSample as exploratory diagnostics of approximation behavior and runtime, not as theorem-facing evidence when no exact cross-family certificate is available; heavier stress tests are archived in the appendix and artifact package.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.21399v1</id>\n <title>The Myhill-Nerode Theorem for Bounded Interaction: Canonical Abstractions via Agent-Bounded Indistinguishability</title>\n <updated>2026-03-22T20:59:31Z</updated>\n <link href='https://arxiv.org/abs/2603.21399v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.21399v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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. For clock-aware probes, it is exactly decision-sufficient for objectives that depend only on the agent's observations and actions; for latent-state rewards, we use an observation-Lipschitz approximation bound. The main theorem object is the clock-aware quotient; scalable deterministic-stationary experiments study a tractable coarsening with gap measured on small exact cases and explored empirically at larger scale. We validate theorem-level claims on Tiger and GridWorld. We also report operational case studies on Tiger, GridWorld, and RockSample as exploratory diagnostics of approximation behavior and runtime, not as theorem-facing evidence when no exact cross-family certificate is available; heavier stress tests are archived in the appendix and artifact package.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-03-22T20:59:31Z</published>\n <arxiv:comment>43 pages, 4 figures, 23 tables. Code: https://github.com/alch3mistdev/finite-pomdp-abstraction (v0.1.1)</arxiv:comment>\n <arxiv:primary_category term='cs.AI'/>\n <author>\n <name>Anthony T. Nixon</name>\n </author>\n </entry>"
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