{"paper":{"title":"Observers, Symmetries, and the Hierarchy of Language Classes: A Theory of Computation Parameterized by the Observer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.FL","authors_text":"Fabio F.G. Buono","submitted_at":"2026-06-25T08:34:09Z","abstract_excerpt":"We introduce the \\emph{observational hierarchy}, a new axis of classification for formal languages, orthogonal to the Chomsky hierarchy. An observer is a function $O : \\Sigma^* \\to S$ that determines which information about the input is accessible to a computational system. The order-blind automaton, which perceives the input as a multiset of symbols rather than a sequence, constitutes the paradigmatic case. We prove that the class of languages recognisable by any machine equipped with such an observer coincides exactly with the permutation-closed languages. We then define a partial order on o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27407","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27407/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}