{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:N2WDLGIUUXID5Z4O6ID5C5HZZE","short_pith_number":"pith:N2WDLGIU","canonical_record":{"source":{"id":"1608.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-02T16:33:21Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"2e2768f70745aff998ede8937bef62463810f18894c5b7706d2d372e15f70a38","abstract_canon_sha256":"f5dad41a9a190ed298a5475572979d5b09d810cb08dbe0efce4168129d446955"},"schema_version":"1.0"},"canonical_sha256":"6eac359914a5d03ee78ef207d174f9c92add6f770208b1d13f6fe81adf88ebc8","source":{"kind":"arxiv","id":"1608.00889","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00889","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00889v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00889","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"N2WDLGIUUXID","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N2WDLGIUUXID5Z4O","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N2WDLGIU","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:N2WDLGIUUXID5Z4O6ID5C5HZZE","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00889","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-02T16:33:21Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"2e2768f70745aff998ede8937bef62463810f18894c5b7706d2d372e15f70a38","abstract_canon_sha256":"f5dad41a9a190ed298a5475572979d5b09d810cb08dbe0efce4168129d446955"},"schema_version":"1.0"},"canonical_sha256":"6eac359914a5d03ee78ef207d174f9c92add6f770208b1d13f6fe81adf88ebc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:27.194169Z","signature_b64":"nF9jOzohmCnfdyPwmvJjtL49g2N8iXs4xjju7Ewv/4VZWAg20doS3JMWz1XipNppsEvmA1EiEbxFVRfDcnqtCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6eac359914a5d03ee78ef207d174f9c92add6f770208b1d13f6fe81adf88ebc8","last_reissued_at":"2026-05-18T01:04:27.193493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:27.193493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00889","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H1gzZgGRuxNNyd+jUViL7jlyJQfq+/aPLtolMhHLXMNWolD8eLUfAoLwRodfQjM8cxA/eNTHSw6aMoMIRPPgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:17:19.940815Z"},"content_sha256":"82504c490ac1f2dc49f907bfdd64cc1b316777aadc5bda35921383e0d909b13f","schema_version":"1.0","event_id":"sha256:82504c490ac1f2dc49f907bfdd64cc1b316777aadc5bda35921383e0d909b13f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:N2WDLGIUUXID5Z4O6ID5C5HZZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating the Maximum Number of Synchronizing States in Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.FL","authors_text":"Andrew Ryzhikov","submitted_at":"2016-08-02T16:33:21Z","abstract_excerpt":"We consider the problem {\\sc Max Sync Set} of finding a maximum synchronizing set of states in a given automaton. We show that the decision version of this problem is PSPACE-complete and investigate the approximability of {\\sc Max Sync Set} for binary and weakly acyclic automata (an automaton is called weakly acyclic if it contains no cycles other than self-loops). We prove that, assuming $P \\ne NP$, for any $\\varepsilon > 0$, the {\\sc Max Sync Set} problem cannot be approximated in polynomial time within a factor of $O(n^{1 - \\varepsilon})$ for weakly acyclic $n$-state automata with alphabet "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00889","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrgTPvHLtq3g4atm1Ee9r8sys1A+rz64felF86L6VEWsVQ92rceNR1hzonh0bHTUnTWHQyVJLQdPIIL8jZyhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:17:19.941490Z"},"content_sha256":"642e54b3ec842481dca004ab5f7418e6743aaa1d425691a42aba1ba57bb61cac","schema_version":"1.0","event_id":"sha256:642e54b3ec842481dca004ab5f7418e6743aaa1d425691a42aba1ba57bb61cac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/bundle.json","state_url":"https://pith.science/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T20:17:19Z","links":{"resolver":"https://pith.science/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE","bundle":"https://pith.science/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/bundle.json","state":"https://pith.science/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2WDLGIUUXID5Z4O6ID5C5HZZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N2WDLGIUUXID5Z4O6ID5C5HZZE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f5dad41a9a190ed298a5475572979d5b09d810cb08dbe0efce4168129d446955","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-02T16:33:21Z","title_canon_sha256":"2e2768f70745aff998ede8937bef62463810f18894c5b7706d2d372e15f70a38"},"schema_version":"1.0","source":{"id":"1608.00889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00889","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00889v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00889","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"N2WDLGIUUXID","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N2WDLGIUUXID5Z4O","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N2WDLGIU","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:642e54b3ec842481dca004ab5f7418e6743aaa1d425691a42aba1ba57bb61cac","target":"graph","created_at":"2026-05-18T01:04:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the problem {\\sc Max Sync Set} of finding a maximum synchronizing set of states in a given automaton. We show that the decision version of this problem is PSPACE-complete and investigate the approximability of {\\sc Max Sync Set} for binary and weakly acyclic automata (an automaton is called weakly acyclic if it contains no cycles other than self-loops). We prove that, assuming $P \\ne NP$, for any $\\varepsilon > 0$, the {\\sc Max Sync Set} problem cannot be approximated in polynomial time within a factor of $O(n^{1 - \\varepsilon})$ for weakly acyclic $n$-state automata with alphabet ","authors_text":"Andrew Ryzhikov","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-02T16:33:21Z","title":"Approximating the Maximum Number of Synchronizing States in Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00889","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:82504c490ac1f2dc49f907bfdd64cc1b316777aadc5bda35921383e0d909b13f","target":"record","created_at":"2026-05-18T01:04:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f5dad41a9a190ed298a5475572979d5b09d810cb08dbe0efce4168129d446955","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2016-08-02T16:33:21Z","title_canon_sha256":"2e2768f70745aff998ede8937bef62463810f18894c5b7706d2d372e15f70a38"},"schema_version":"1.0","source":{"id":"1608.00889","kind":"arxiv","version":2}},"canonical_sha256":"6eac359914a5d03ee78ef207d174f9c92add6f770208b1d13f6fe81adf88ebc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eac359914a5d03ee78ef207d174f9c92add6f770208b1d13f6fe81adf88ebc8","first_computed_at":"2026-05-18T01:04:27.193493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.193493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nF9jOzohmCnfdyPwmvJjtL49g2N8iXs4xjju7Ewv/4VZWAg20doS3JMWz1XipNppsEvmA1EiEbxFVRfDcnqtCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.194169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82504c490ac1f2dc49f907bfdd64cc1b316777aadc5bda35921383e0d909b13f","sha256:642e54b3ec842481dca004ab5f7418e6743aaa1d425691a42aba1ba57bb61cac"],"state_sha256":"b6d9ba96ebc61d40b9ec3e0e71db7e71c34d299d3b9ae3c809e894159df54bdc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aPkzKM+SVIzLsWtc0ORMsQK7Amq49nlVNECVvnkc0X/djxFHrWtJXd4ioJRdoe30YjTpMJ57CW5d8CX/xm4KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:17:19.944962Z","bundle_sha256":"c4be718a9fda461ccd6f1e15c16e579d621b8dd8aca20d816b42479959dd7877"}}