{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HEBCDDUDT27P3WURVVCKFLMULN","short_pith_number":"pith:HEBCDDUD","schema_version":"1.0","canonical_sha256":"3902218e839ebefdda91ad44a2ad945b6305e7c0d3a5999fbfd69fb1efc27140","source":{"kind":"arxiv","id":"1703.05016","version":1},"attestation_state":"computed","paper":{"title":"Complexity of Infimal Observable Superlanguages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.SY","authors_text":"Tom\\'a\\v{s} Masopust","submitted_at":"2017-03-15T08:55:50Z","abstract_excerpt":"The infimal prefix-closed, controllable and observable superlanguage plays an essential role in the relationship between controllability, observability and co-observability -- the central notions of supervisory control theory. Existing algorithms for its computation are exponential and it is not known whether a polynomial algorithm exists. In this paper, we study the state complexity of this language. State complexity of a language is the number of states of the minimal DFA for the language. For a language of state complexity $n$, we show that the upper-bound state complexity on the infimal pr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.05016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-03-15T08:55:50Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"e43df012f48b8c59ad6bcd997bc5d1f45eb33c3a4ca2bda64bf9a08e86049010","abstract_canon_sha256":"418b47a8afa3c07bd358c3149bd34e4eaa3ec2b2b632cd4a391fc58828f66492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:38.583514Z","signature_b64":"MhdLoG+eHFbFgEBxRCCPhRsaleQHKt9OnksaegaBRGVfpvyE5o2GQz3RY/IpDN9yWUdn2ibvHhmRSwkdlGDpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3902218e839ebefdda91ad44a2ad945b6305e7c0d3a5999fbfd69fb1efc27140","last_reissued_at":"2026-05-18T00:48:38.582916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:38.582916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complexity of Infimal Observable Superlanguages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.SY","authors_text":"Tom\\'a\\v{s} Masopust","submitted_at":"2017-03-15T08:55:50Z","abstract_excerpt":"The infimal prefix-closed, controllable and observable superlanguage plays an essential role in the relationship between controllability, observability and co-observability -- the central notions of supervisory control theory. Existing algorithms for its computation are exponential and it is not known whether a polynomial algorithm exists. In this paper, we study the state complexity of this language. State complexity of a language is the number of states of the minimal DFA for the language. For a language of state complexity $n$, we show that the upper-bound state complexity on the infimal pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05016","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.05016","created_at":"2026-05-18T00:48:38.583003+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.05016v1","created_at":"2026-05-18T00:48:38.583003+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05016","created_at":"2026-05-18T00:48:38.583003+00:00"},{"alias_kind":"pith_short_12","alias_value":"HEBCDDUDT27P","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HEBCDDUDT27P3WUR","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HEBCDDUD","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN","json":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN.json","graph_json":"https://pith.science/api/pith-number/HEBCDDUDT27P3WURVVCKFLMULN/graph.json","events_json":"https://pith.science/api/pith-number/HEBCDDUDT27P3WURVVCKFLMULN/events.json","paper":"https://pith.science/paper/HEBCDDUD"},"agent_actions":{"view_html":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN","download_json":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN.json","view_paper":"https://pith.science/paper/HEBCDDUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.05016&json=true","fetch_graph":"https://pith.science/api/pith-number/HEBCDDUDT27P3WURVVCKFLMULN/graph.json","fetch_events":"https://pith.science/api/pith-number/HEBCDDUDT27P3WURVVCKFLMULN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN/action/storage_attestation","attest_author":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN/action/author_attestation","sign_citation":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN/action/citation_signature","submit_replication":"https://pith.science/pith/HEBCDDUDT27P3WURVVCKFLMULN/action/replication_record"}},"created_at":"2026-05-18T00:48:38.583003+00:00","updated_at":"2026-05-18T00:48:38.583003+00:00"}