{"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"}