{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BPIZMDBFHESRVZRK27CERTGHXH","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":"3995eab4d66a34fc545173d94219ae6b68b1312c15414e18393f5a3336638f71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-07-22T22:13:12Z","title_canon_sha256":"245f2ef0e293ecbe29c552d4cec0e8ebde20ccde46d4411158dbf45f1326d506"},"schema_version":"1.0","source":{"id":"1007.4018","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4018","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4018v2","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4018","created_at":"2026-05-18T01:37:39Z"},{"alias_kind":"pith_short_12","alias_value":"BPIZMDBFHESR","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BPIZMDBFHESRVZRK","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BPIZMDBF","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:21b958b436163b62f32d3c73d86fd3174ff67b8b154c3c2684b89e6a0dd90d4a","target":"graph","created_at":"2026-05-18T01:37:39Z","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":"Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages~$L$ that assign to each word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word $w$ is the supremum of the values of the runs over $w$. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be non-$\\omega$-regul","authors_text":"EPFL Switzerland), Krishnendu Chatterjee (IST Austria), Laurent Doyen (CNRS France), Thomas A Henzinger (IST Austria","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-07-22T22:13:12Z","title":"Expressiveness and Closure Properties for Quantitative Languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4018","kind":"arxiv","version":2},"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:eedb15cb3ffef3f7fd4e675f96e0fa660876f0c69d0113b845d6b4a0722c407c","target":"record","created_at":"2026-05-18T01:37:39Z","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":"3995eab4d66a34fc545173d94219ae6b68b1312c15414e18393f5a3336638f71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2010-07-22T22:13:12Z","title_canon_sha256":"245f2ef0e293ecbe29c552d4cec0e8ebde20ccde46d4411158dbf45f1326d506"},"schema_version":"1.0","source":{"id":"1007.4018","kind":"arxiv","version":2}},"canonical_sha256":"0bd1960c2539251ae62ad7c448ccc7b9c2c285eddbe9583bdb70f97c6615100f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bd1960c2539251ae62ad7c448ccc7b9c2c285eddbe9583bdb70f97c6615100f","first_computed_at":"2026-05-18T01:37:39.944676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:39.944676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0kLIRM361/6Z2GuNAMzLEjFkGMPaoktrSLisvtUy0jlzDU8mTVPOar7TM4ygiB+oerF3E7oiFufwdIqy6JprDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:39.945334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4018","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eedb15cb3ffef3f7fd4e675f96e0fa660876f0c69d0113b845d6b4a0722c407c","sha256:21b958b436163b62f32d3c73d86fd3174ff67b8b154c3c2684b89e6a0dd90d4a"],"state_sha256":"48a47a1d40104c8ef60f147c774e7dd87b36e69d90af663ab4a2ff3ebe117cde"}