{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O7AANIIWTPKDSUE3WRG2UQHHIT","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":"9af804c56bc07fc51aab25fa7f8bd9ae8b139bf2737e13fd902fad99a2f42747","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-23T07:29:22Z","title_canon_sha256":"de29abf2bcbfb871e0f0aa2fe3701b812f390e919d19a026156735c3ad674d78"},"schema_version":"1.0","source":{"id":"1204.4982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4982","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4982v1","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4982","created_at":"2026-05-18T03:57:15Z"},{"alias_kind":"pith_short_12","alias_value":"O7AANIIWTPKD","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O7AANIIWTPKDSUE3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O7AANIIW","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:26f42ece5557ebec297ed43d24a97d6f9ea555950c80543c03aebeeeff89e618","target":"graph","created_at":"2026-05-18T03:57:15Z","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":"In this chapter we discuss the problem of enumerating distinct regular expressions by size and the regular languages they represent. We discuss various notions of the size of a regular expression that appear in the literature and their advantages and disadvantages. We consider a formal definition of regular expressions using a context-free grammar.\n  We then show how to enumerate strings generated by an unambiguous context-free grammar using the Chomsky-Sch\\\"utzenberger theorem. This theorem allows one to construct an algebraic equation whose power series expansion provides the enumeration. Cl","authors_text":"Hermann Gruber, Jeffrey Shallit, Jonathan Lee","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-23T07:29:22Z","title":"Enumerating regular expressions and their languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4982","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:d1dcbb42c46b1d9d2a7e9959606ce3a21eae20423f50d21200165c03e579ee7c","target":"record","created_at":"2026-05-18T03:57:15Z","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":"9af804c56bc07fc51aab25fa7f8bd9ae8b139bf2737e13fd902fad99a2f42747","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2012-04-23T07:29:22Z","title_canon_sha256":"de29abf2bcbfb871e0f0aa2fe3701b812f390e919d19a026156735c3ad674d78"},"schema_version":"1.0","source":{"id":"1204.4982","kind":"arxiv","version":1}},"canonical_sha256":"77c006a1169bd439509bb44daa40e744e34f4cc47a58378e9b48d22fec94b41f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77c006a1169bd439509bb44daa40e744e34f4cc47a58378e9b48d22fec94b41f","first_computed_at":"2026-05-18T03:57:15.024182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:15.024182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fh++T5Wg6zERCWhncSCwyxPvcPegsj1GL2dRYacXxALdS0/v7o2L2azFNXch+wFbIziAgJh4EgmbzQzgJzNCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:15.024898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1dcbb42c46b1d9d2a7e9959606ce3a21eae20423f50d21200165c03e579ee7c","sha256:26f42ece5557ebec297ed43d24a97d6f9ea555950c80543c03aebeeeff89e618"],"state_sha256":"298a277b746278b6c05e9d3478ac5f2f657f236b4448b1f144f82085e37f1c3b"}