{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SWR6OME3OHY3C6X7NF3R2KT2Q5","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":"c3891bcd3f03025a7d17af93cf2bba2ac28b2d5e2319b997ced16c60bffb54b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2018-02-21T01:47:25Z","title_canon_sha256":"b9bee462590c72c8b92f9d498bf1a217071ccc8ba37fe46ed759f9646a3c783f"},"schema_version":"1.0","source":{"id":"1802.07397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07397","created_at":"2026-05-18T00:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07397v1","created_at":"2026-05-18T00:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07397","created_at":"2026-05-18T00:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"SWR6OME3OHY3","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SWR6OME3OHY3C6X7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SWR6OME3","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:169a3b8dd13726875b2044d82f6ec0497a6b5ae527cd7fcf93326b69fd33cf52","target":"graph","created_at":"2026-05-18T00:22:50Z","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 introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of upward closed sets. In this way, a range of regular language classes arises as PTLs. Moreover, each of the WQOs guarantees regularity of all downward closed sets. We consider two problems. First, we study which (perhaps non-regular) language classes permit a decision procedure to decide whether two given languages are separable by a PTL with respect to a given","authors_text":"Georg Zetzsche","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2018-02-21T01:47:25Z","title":"PTL-separability and closures for WQOs on words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07397","kind":"arxiv","version":1},"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:f94e816efb4b7fed39cd868303a11a83435a52fccc0c84869c60226dee02c0b7","target":"record","created_at":"2026-05-18T00:22:50Z","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":"c3891bcd3f03025a7d17af93cf2bba2ac28b2d5e2319b997ced16c60bffb54b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2018-02-21T01:47:25Z","title_canon_sha256":"b9bee462590c72c8b92f9d498bf1a217071ccc8ba37fe46ed759f9646a3c783f"},"schema_version":"1.0","source":{"id":"1802.07397","kind":"arxiv","version":1}},"canonical_sha256":"95a3e7309b71f1b17aff69771d2a7a8772b4f8f7eb8e7e0bb2cdff35576cec56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95a3e7309b71f1b17aff69771d2a7a8772b4f8f7eb8e7e0bb2cdff35576cec56","first_computed_at":"2026-05-18T00:22:50.336492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:50.336492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fuWSe39sm+w82eE1+XXbqR+TvS2iCMOvQb01X9xAhQcYImIINNyeSQ2aQeGexr5s4OCJs+3ajKBDm1/eYg+pAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:50.337221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f94e816efb4b7fed39cd868303a11a83435a52fccc0c84869c60226dee02c0b7","sha256:169a3b8dd13726875b2044d82f6ec0497a6b5ae527cd7fcf93326b69fd33cf52"],"state_sha256":"9e287becb602488ed55519dab4a4ff98e9944eebac45b9d2fb81f57f5cdbad23"}