{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6LPAKZTLX6CS5DDUV6SKAJYMA5","short_pith_number":"pith:6LPAKZTL","schema_version":"1.0","canonical_sha256":"f2de05666bbf852e8c74afa4a0270c0741e555708acfc647bdf7d84286e19289","source":{"kind":"arxiv","id":"1609.06379","version":1},"attestation_state":"computed","paper":{"title":"Global Caching for the Alternation-free $\\mu$-Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Christoph Egger, Daniel Hausmann, Lutz Schr\\\"oder","submitted_at":"2016-09-20T22:56:46Z","abstract_excerpt":"We present a sound, complete, and optimal single-pass tableau algorithm for the alternation-free $\\mu$-calculus. The algorithm supports global caching with intermediate propagation and runs in time $2^{\\mathcal{O}(n)}$. In game-theoretic terms, our algorithm integrates the steps for constructing and solving the B\\\"uchi game arising from the input tableau into a single procedure; this is done on-the-fly, i.e. may terminate before the game has been fully constructed. This suggests a slogan to the effect that global caching = game solving on-the-fly. A prototypical implementation shows promising "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.06379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-09-20T22:56:46Z","cross_cats_sorted":[],"title_canon_sha256":"32baa3281d2a9482c14a9d2922433612878a85de2ab1be9918b52b8e336ce353","abstract_canon_sha256":"c013d77690d828611b69648d299f191d3182d39a1891a5c1a6af55ed4391e4a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:08.480573Z","signature_b64":"xYafUJiMoN5xF+Q8e2t/jdlbhQ/XZBPzNGNb7vDNDNsXHDV2TJNv47mVuPm0YyludYFQD35799spSkyh7SgHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2de05666bbf852e8c74afa4a0270c0741e555708acfc647bdf7d84286e19289","last_reissued_at":"2026-05-18T01:04:08.479937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:08.479937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Caching for the Alternation-free $\\mu$-Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Christoph Egger, Daniel Hausmann, Lutz Schr\\\"oder","submitted_at":"2016-09-20T22:56:46Z","abstract_excerpt":"We present a sound, complete, and optimal single-pass tableau algorithm for the alternation-free $\\mu$-calculus. The algorithm supports global caching with intermediate propagation and runs in time $2^{\\mathcal{O}(n)}$. In game-theoretic terms, our algorithm integrates the steps for constructing and solving the B\\\"uchi game arising from the input tableau into a single procedure; this is done on-the-fly, i.e. may terminate before the game has been fully constructed. This suggests a slogan to the effect that global caching = game solving on-the-fly. A prototypical implementation shows promising "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06379","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.06379","created_at":"2026-05-18T01:04:08.480016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.06379v1","created_at":"2026-05-18T01:04:08.480016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06379","created_at":"2026-05-18T01:04:08.480016+00:00"},{"alias_kind":"pith_short_12","alias_value":"6LPAKZTLX6CS","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6LPAKZTLX6CS5DDU","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6LPAKZTL","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5","json":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5.json","graph_json":"https://pith.science/api/pith-number/6LPAKZTLX6CS5DDUV6SKAJYMA5/graph.json","events_json":"https://pith.science/api/pith-number/6LPAKZTLX6CS5DDUV6SKAJYMA5/events.json","paper":"https://pith.science/paper/6LPAKZTL"},"agent_actions":{"view_html":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5","download_json":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5.json","view_paper":"https://pith.science/paper/6LPAKZTL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.06379&json=true","fetch_graph":"https://pith.science/api/pith-number/6LPAKZTLX6CS5DDUV6SKAJYMA5/graph.json","fetch_events":"https://pith.science/api/pith-number/6LPAKZTLX6CS5DDUV6SKAJYMA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5/action/storage_attestation","attest_author":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5/action/author_attestation","sign_citation":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5/action/citation_signature","submit_replication":"https://pith.science/pith/6LPAKZTLX6CS5DDUV6SKAJYMA5/action/replication_record"}},"created_at":"2026-05-18T01:04:08.480016+00:00","updated_at":"2026-05-18T01:04:08.480016+00:00"}