{"paper":{"title":"Distributional Learning of Graph Languages Generated by Fixed-Interface Clause Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Fixed-parameter graph languages generated by clause systems are learnable in the limit from positive data and membership queries.","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Satoshi Matsumoto, Takayoshi Shoudai, Tomoyuki Uchida, Yusuke Suzuki","submitted_at":"2026-04-29T06:32:34Z","abstract_excerpt":"Distributional learning provides a useful framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems (FICSs).\n  We formulate FICSs explicitly and study the corresponding learning problem under positive presentations and membership queries. We consider a bounded class of graph languages satisfying the finite context property (FCP) under a bounded-degree assumption. The bounds are expressed by the degree bound $\\Delta$ together with five structural parameters $m,s,t,w$,"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Hence, for every fixed parameter tuple (Δ,m,s,t,w,d), the target language is identifiable in the limit from positive data and membership queries. We also prove that the learner has polynomial-time update on FICSL^FCP_Δ(m,s,t,w,d).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The target language belongs to the bounded class FICSL^FCP_Δ(m,s,t,w,d) that satisfies the finite context property under the bounded-degree assumption.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Graph languages from fixed-interface clause systems with the finite context property are identifiable in the limit from positive data and membership queries by a polynomial-time learner for any fixed bound tuple (Δ,m,s,t,w,d).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Fixed-parameter graph languages generated by clause systems are learnable in the limit from positive data and membership queries.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c6b39314efee040693d79f36ce61ff9950981c89d0f4a6ae92bff32850df8fc1"},"source":{"id":"2604.26333","kind":"arxiv","version":2},"verdict":{"id":"7f220e77-9807-4942-9061-14494796662a","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:51:25.636595Z","strongest_claim":"Hence, for every fixed parameter tuple (Δ,m,s,t,w,d), the target language is identifiable in the limit from positive data and membership queries. We also prove that the learner has polynomial-time update on FICSL^FCP_Δ(m,s,t,w,d).","one_line_summary":"Graph languages from fixed-interface clause systems with the finite context property are identifiable in the limit from positive data and membership queries by a polynomial-time learner for any fixed bound tuple (Δ,m,s,t,w,d).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The target language belongs to the bounded class FICSL^FCP_Δ(m,s,t,w,d) that satisfies the finite context property under the bounded-degree assumption.","pith_extraction_headline":"Fixed-parameter graph languages generated by clause systems are learnable in the limit from positive data and membership queries."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26333/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T00:38:40.881092Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:13:47.209774Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"32be678a675d3c60ec50d7f1e644ff3ce03e63e32e9b8aacb49d9fb1cca2a482"},"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"}