{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4G5RWNVDRVO72EQXQWMZY3YYXV","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":"2ed0ebe72b8c8428137ddb715567135d165fc8e77bc6b5f09b89065a3082a914","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-03-30T20:38:23Z","title_canon_sha256":"337440ba229b3358e4c09472fed8ba22a5e59a7a32a1426470583a73c81eda81"},"schema_version":"1.0","source":{"id":"1503.08847","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08847","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08847v3","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08847","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"4G5RWNVDRVO7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4G5RWNVDRVO72EQX","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4G5RWNVD","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:ce5bd29935b2c39e26716f2f8fe04758745b7cb57c3caf7e402782db278ebdd2","target":"graph","created_at":"2026-05-18T01:36:47Z","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":"There are languages A such that there is a Pushdown Automata (PDA) that recognizes A which is much smaller than any Deterministic Pushdown Automata (DPDA) that recognizes A. There are languages A such that there is a Linear Bounded Automata (Linear Space Turing Machine, henceforth LBA) that recognizes A which is much smaller than ny PDA that recognizes A. There are languages A such that both A and compliment(A) are recognizable by a PDA, but the PDA for A is much smaller than the PDA for compliment(A). There are languages A1, A2 such that A1,A2,A1 INTERSECT A_2 are recognizable by a PDA, but t","authors_text":"Richard Beigel, William Gasarch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-03-30T20:38:23Z","title":"On the Sizes of DPDAs, PDAs, LBAs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08847","kind":"arxiv","version":3},"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":"sha256:3a9cacee5d44d8cc819ac819e84dc6f36f28310e1feff813085290236ab15db9","target":"record","created_at":"2026-05-18T01:36:47Z","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":"2ed0ebe72b8c8428137ddb715567135d165fc8e77bc6b5f09b89065a3082a914","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2015-03-30T20:38:23Z","title_canon_sha256":"337440ba229b3358e4c09472fed8ba22a5e59a7a32a1426470583a73c81eda81"},"schema_version":"1.0","source":{"id":"1503.08847","kind":"arxiv","version":3}},"canonical_sha256":"e1bb1b36a38d5dfd121785999c6f18bd62f748c4083e61d6b40b14c8295f3d8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1bb1b36a38d5dfd121785999c6f18bd62f748c4083e61d6b40b14c8295f3d8a","first_computed_at":"2026-05-18T01:36:47.914492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:47.914492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D9wiSpyIJr41v6k1vYqpv8GmBxvxNBiqucap00/QHzRIlXaJWZJxsQ04hQIbm1+cw4i2fxlQfttn9POk7I76CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:47.915071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08847","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a9cacee5d44d8cc819ac819e84dc6f36f28310e1feff813085290236ab15db9","sha256:ce5bd29935b2c39e26716f2f8fe04758745b7cb57c3caf7e402782db278ebdd2"],"state_sha256":"03733e70ab5e03452f4510a43d0a4c93fb6b0c5fe0bd342c8255bf16ba768c62"}