{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:5HN7DHFJF4RC5J7GN6TK3SWNXG","short_pith_number":"pith:5HN7DHFJ","canonical_record":{"source":{"id":"cs/0702120","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2007-02-21T16:14:34Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8ba06bbd92548ffe1e10efb786bb60134609fdf30f2245774d3391f9e9cbc291","abstract_canon_sha256":"0a5c5069dce9db3d8366d35b8e76d6ecf1881d4dac8cd0100147e55ddce284ba"},"schema_version":"1.0"},"canonical_sha256":"e9dbf19ca92f222ea7e66fa6adcacdb998249a5a2b725c91decd05bbc5594582","source":{"kind":"arxiv","id":"cs/0702120","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0702120","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0702120v3","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0702120","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"5HN7DHFJF4RC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5HN7DHFJF4RC5J7G","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5HN7DHFJ","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:5HN7DHFJF4RC5J7GN6TK3SWNXG","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0702120","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2007-02-21T16:14:34Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"8ba06bbd92548ffe1e10efb786bb60134609fdf30f2245774d3391f9e9cbc291","abstract_canon_sha256":"0a5c5069dce9db3d8366d35b8e76d6ecf1881d4dac8cd0100147e55ddce284ba"},"schema_version":"1.0"},"canonical_sha256":"e9dbf19ca92f222ea7e66fa6adcacdb998249a5a2b725c91decd05bbc5594582","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:03.227899Z","signature_b64":"OItEiZ00w+1KxbYiKPiFZg4KWQjGUFWM0zUQJmWqRNCQQxEto8c4KN7pUuhLelZsHdpl39attIbPHCNhGd75AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9dbf19ca92f222ea7e66fa6adcacdb998249a5a2b725c91decd05bbc5594582","last_reissued_at":"2026-05-18T00:53:03.227488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:03.227488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0702120","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDCXmjuUKiNAEAHPP5MoMApBU7MI7KoY3Y8TtsX1Rc+ZkaObHwqrWj+W4lugTZnxyxW4grqKG2GGRMkCKw/DBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:09:42.027740Z"},"content_sha256":"fd7951700b78fe40beeb794f75fcff53f1911d0a91f8efcd58846c05d9db5f2c","schema_version":"1.0","event_id":"sha256:fd7951700b78fe40beeb794f75fcff53f1911d0a91f8efcd58846c05d9db5f2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:5HN7DHFJF4RC5J7GN6TK3SWNXG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the decidability and complexity of Metric Temporal Logic over finite words","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"James Worrell, Joel Ouaknine","submitted_at":"2007-02-21T16:14:34Z","abstract_excerpt":"Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. Thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702120","kind":"arxiv","version":3},"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":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8dc3UJf96ja51eX56Km1K+aZ0Rc9IxYWgAR7/BMpA4HsHc8EiHnwQ9WZ4Bm7IYRi96Iw1EvBJiPT9n+nBOxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:09:42.028431Z"},"content_sha256":"a42dd25f10792d2f78510fb91363379a1f76ea50e55d50604667ebd98ba545c1","schema_version":"1.0","event_id":"sha256:a42dd25f10792d2f78510fb91363379a1f76ea50e55d50604667ebd98ba545c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/bundle.json","state_url":"https://pith.science/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/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":"2026-05-28T21:09:42Z","links":{"resolver":"https://pith.science/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG","bundle":"https://pith.science/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/bundle.json","state":"https://pith.science/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HN7DHFJF4RC5J7GN6TK3SWNXG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:5HN7DHFJF4RC5J7GN6TK3SWNXG","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":"0a5c5069dce9db3d8366d35b8e76d6ecf1881d4dac8cd0100147e55ddce284ba","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"cs.LO","submitted_at":"2007-02-21T16:14:34Z","title_canon_sha256":"8ba06bbd92548ffe1e10efb786bb60134609fdf30f2245774d3391f9e9cbc291"},"schema_version":"1.0","source":{"id":"cs/0702120","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0702120","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0702120v3","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0702120","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"5HN7DHFJF4RC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5HN7DHFJF4RC5J7G","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5HN7DHFJ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a42dd25f10792d2f78510fb91363379a1f76ea50e55d50604667ebd98ba545c1","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL--which includes invariance and time-bounded response properties--is also decidable. Thes","authors_text":"James Worrell, Joel Ouaknine","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"cs.LO","submitted_at":"2007-02-21T16:14:34Z","title":"On the decidability and complexity of Metric Temporal Logic over finite words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0702120","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:fd7951700b78fe40beeb794f75fcff53f1911d0a91f8efcd58846c05d9db5f2c","target":"record","created_at":"2026-05-18T00:53:03Z","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":"0a5c5069dce9db3d8366d35b8e76d6ecf1881d4dac8cd0100147e55ddce284ba","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"cs.LO","submitted_at":"2007-02-21T16:14:34Z","title_canon_sha256":"8ba06bbd92548ffe1e10efb786bb60134609fdf30f2245774d3391f9e9cbc291"},"schema_version":"1.0","source":{"id":"cs/0702120","kind":"arxiv","version":3}},"canonical_sha256":"e9dbf19ca92f222ea7e66fa6adcacdb998249a5a2b725c91decd05bbc5594582","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9dbf19ca92f222ea7e66fa6adcacdb998249a5a2b725c91decd05bbc5594582","first_computed_at":"2026-05-18T00:53:03.227488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.227488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OItEiZ00w+1KxbYiKPiFZg4KWQjGUFWM0zUQJmWqRNCQQxEto8c4KN7pUuhLelZsHdpl39attIbPHCNhGd75AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.227899Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0702120","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd7951700b78fe40beeb794f75fcff53f1911d0a91f8efcd58846c05d9db5f2c","sha256:a42dd25f10792d2f78510fb91363379a1f76ea50e55d50604667ebd98ba545c1"],"state_sha256":"290cf63ab06a12dabc3bd61d23f900f0abcebf970f6b9c82299f6fb31c01aab3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wc7hSWj2oT0XkHdFkBfY6Ww5myqss+ojk43lDgroF0AF23ede6yVzYPStBeiiWx2qptyCUCBEeG6DHy8Mr+8DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:09:42.032252Z","bundle_sha256":"ac58c18fffe5445a645f5439937a5aef61001b4bce93f14c18d37721b2381ba6"}}