{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D6I6MO6MUJT6RAJWOPB3XUARK7","short_pith_number":"pith:D6I6MO6M","canonical_record":{"source":{"id":"1702.05024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-02-16T15:55:37Z","cross_cats_sorted":[],"title_canon_sha256":"b8da7edf8272418e51856574e2b3b1053960cff13064c7c0e61491205ac94655","abstract_canon_sha256":"4f30e9b52d5500ed76c785db332015088fa9a22168ec2ebfdf1a11341cfdedf1"},"schema_version":"1.0"},"canonical_sha256":"1f91e63bcca267e8813673c3bbd01157f52f677c76cba083fc7c3e00ae710bf7","source":{"kind":"arxiv","id":"1702.05024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05024","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05024v1","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05024","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"D6I6MO6MUJT6","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6I6MO6MUJT6RAJW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6I6MO6M","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D6I6MO6MUJT6RAJWOPB3XUARK7","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-02-16T15:55:37Z","cross_cats_sorted":[],"title_canon_sha256":"b8da7edf8272418e51856574e2b3b1053960cff13064c7c0e61491205ac94655","abstract_canon_sha256":"4f30e9b52d5500ed76c785db332015088fa9a22168ec2ebfdf1a11341cfdedf1"},"schema_version":"1.0"},"canonical_sha256":"1f91e63bcca267e8813673c3bbd01157f52f677c76cba083fc7c3e00ae710bf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:36.427227Z","signature_b64":"WYb3xzBnL8vuN0b/7cgm+OCIqvppaPfqT0xDVx1kwp+vUXf8TEyBoNJ8zn+lScX7HWMMDvhoehoE68Ao9yUvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f91e63bcca267e8813673c3bbd01157f52f677c76cba083fc7c3e00ae710bf7","last_reissued_at":"2026-05-18T00:50:36.426670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:36.426670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05024","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OagWSy0YQeEjKmGtCF+Z3t+Z+sFvlQ+AI16nvKYMcf9SubxiiOSouYtTB23hvokd1XdNIENsQTZHjIhHSdR9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:28:27.268333Z"},"content_sha256":"15637a8d5cb3bb62d84663dbf9bf2033e230b41e309520e34984cdd627fd68a3","schema_version":"1.0","event_id":"sha256:15637a8d5cb3bb62d84663dbf9bf2033e230b41e309520e34984cdd627fd68a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D6I6MO6MUJT6RAJWOPB3XUARK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a Theory of Complexity of Regular Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Janusz A. Brzozowski","submitted_at":"2017-02-16T15:55:37Z","abstract_excerpt":"We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and is the same as its state complexity -- we also consider the size of its syntactic semigroup and the quotient complexity of its atoms -- basic components of every regular language. We then turn to the study of the quotient/state complexity of common operations on regular languages: reversal, (Kleene) star, product (concatenation) and boolean operations. We exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05024","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l7FPXLKU/MCJHmHB/p0TMhqM1QbDrRrK8sAhWoB+GSg4+AoqWPz3ktsLDZj3ksyjjf0TN10t8olQdo/oSpIvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T09:28:27.268678Z"},"content_sha256":"ffa6a572290ec307b1378030a2537a65ed3af8811bb027d1702250b7007aa179","schema_version":"1.0","event_id":"sha256:ffa6a572290ec307b1378030a2537a65ed3af8811bb027d1702250b7007aa179"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/bundle.json","state_url":"https://pith.science/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/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":"2026-06-28T09:28:27Z","links":{"resolver":"https://pith.science/pith/D6I6MO6MUJT6RAJWOPB3XUARK7","bundle":"https://pith.science/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/bundle.json","state":"https://pith.science/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6I6MO6MUJT6RAJWOPB3XUARK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D6I6MO6MUJT6RAJWOPB3XUARK7","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":"4f30e9b52d5500ed76c785db332015088fa9a22168ec2ebfdf1a11341cfdedf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-02-16T15:55:37Z","title_canon_sha256":"b8da7edf8272418e51856574e2b3b1053960cff13064c7c0e61491205ac94655"},"schema_version":"1.0","source":{"id":"1702.05024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05024","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05024v1","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05024","created_at":"2026-05-18T00:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"D6I6MO6MUJT6","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6I6MO6MUJT6RAJW","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6I6MO6M","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:ffa6a572290ec307b1378030a2537a65ed3af8811bb027d1702250b7007aa179","target":"graph","created_at":"2026-05-18T00:50:36Z","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 survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and is the same as its state complexity -- we also consider the size of its syntactic semigroup and the quotient complexity of its atoms -- basic components of every regular language. We then turn to the study of the quotient/state complexity of common operations on regular languages: reversal, (Kleene) star, product (concatenation) and boolean operations. We exa","authors_text":"Janusz A. Brzozowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-02-16T15:55:37Z","title":"Towards a Theory of Complexity of Regular Languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05024","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":"sha256:15637a8d5cb3bb62d84663dbf9bf2033e230b41e309520e34984cdd627fd68a3","target":"record","created_at":"2026-05-18T00:50:36Z","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":"4f30e9b52d5500ed76c785db332015088fa9a22168ec2ebfdf1a11341cfdedf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2017-02-16T15:55:37Z","title_canon_sha256":"b8da7edf8272418e51856574e2b3b1053960cff13064c7c0e61491205ac94655"},"schema_version":"1.0","source":{"id":"1702.05024","kind":"arxiv","version":1}},"canonical_sha256":"1f91e63bcca267e8813673c3bbd01157f52f677c76cba083fc7c3e00ae710bf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f91e63bcca267e8813673c3bbd01157f52f677c76cba083fc7c3e00ae710bf7","first_computed_at":"2026-05-18T00:50:36.426670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:36.426670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYb3xzBnL8vuN0b/7cgm+OCIqvppaPfqT0xDVx1kwp+vUXf8TEyBoNJ8zn+lScX7HWMMDvhoehoE68Ao9yUvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:36.427227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15637a8d5cb3bb62d84663dbf9bf2033e230b41e309520e34984cdd627fd68a3","sha256:ffa6a572290ec307b1378030a2537a65ed3af8811bb027d1702250b7007aa179"],"state_sha256":"dc95c21fd88f8c1a12d6a45e3437174518e38d97735012ec1d8b424b657e24f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2olWjEzBtYZ77XNBsT3dygHVTAOX/Iehryqi/ZZEfpt57mTG/iI/WTS3usX9VuJynCMUAHAY6tuvPp7dSg1FBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T09:28:27.270515Z","bundle_sha256":"694e43f9ed94f7c6ae1a36119f1ea32e372c058ab3c007549c2b9303c7242b79"}}