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Greedily maximizing the Q-function can produce policies that indefinitely defer task completion for reach-avoid problems, or equivalently, Until specifications, even when the value function is optimal. Building upon recent results decomposing the value function for temporal logic (TL) into a graph of constituent value functions, we construct non-Markovian policies based on state history that avoid this pathology and prove their optimality with respect to the quantitative robustness score for nested Until, Globally, and Globally-Until specifications. We further show how the Q function can serve as a safety filter for complex TL specifications, extending prior results beyond simple avo","title":"Value Functions for Temporal Logic: Optimal Policies and Safety Filters","url":"https://arxiv.org/abs/2605.01051","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.01051v1 Announce Type: cross \nAbstract: While Bellman equations for basic reach, avoid, and reach-avoid problems are well studied, the relationship between value optimality and policy optimality becomes subtle in the undiscounted infinite-horizon setting, particularly for more complicated tasks. Greedily maximizing the Q-function can produce policies that indefinitely defer task completion for reach-avoid problems, or equivalently, Until specifications, even when the value function is optimal. Building upon recent results decomposing the value function for temporal logic (TL) into a graph of constituent value functions, we construct non-Markovian policies based on state history that avoid this pathology and prove their optimality with respect to the quantitative robustness score for nested Until, Globally, and Globally-Until specifications. We further show how the Q function can serve as a safety filter for complex TL specifications, extending prior results beyond simple avo","title":"Value Functions for Temporal Logic: Optimal Policies and Safety Filters","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-06T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.01051"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:85795bfd3077a9a320f7a7eb416e497230fb2351f449efe2fa92599ffc9928a6b914c5e8f2eae48c082d4ba46881a70c9cf2aabf18d2f3eafa6934f9e57b460a","signer":"crovia.substrate","subject":{"observed_at":"2026-05-06T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.01051"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"bee9a1d581b1a0993e87a0e2debba484b5515308bbd9e969f832b2d89343c943","leaf_index":116203,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"fbc4abfaa937a89d8d8b04237f4d50a0e0a447161446cd83f02c848412a66e37","side":"left"},{"sibling":"565eece17bbcc291618557ed1912b96a6f096ea1f2a712b1e05fd5de6f74b9a3","side":"left"},{"sibling":"31f3ec6e8f2f15391e80f8168d42a023a9f82656787baecdbda72191b99f1d9d","side":"right"},{"sibling":"886f844bd22e88d4e1d5bebfdf9eb4c4559d211fa62a53afa3e757c4ad90c9e3","side":"left"},{"sibling":"ae4b4370a46bab977e7c0762771d36d29204ab25bd2f10c987f7d3dcfdb2c150","side":"right"},{"sibling":"ab73ec50dd758491f37bb68fb45a7b70504f405f4656f031adb1a5570f81a528","side":"left"},{"sibling":"f80ae3990cd3c4b61ffd8daa9d6ee7b1b36304ac3557faf836fe49c3e7d7fef2","side":"left"},{"sibling":"337e888c904278e2dba91f3f1f4ea3c78aa6421dad9d2b8e076ce153c74c3f82","side":"left"},{"sibling":"aece872b65a68d3775a2636761a78e8ecbdc28b94538a659e6069c57bef430e0","side":"left"},{"sibling":"fb3602a0ad8c9fcab7b18e13690c40ca4a2f5402557d976d681a369555c04ae2","side":"right"},{"sibling":"ddc060ac400459417799f688c75d5b271636afa40d89ec7fc98652473a8061f6","side":"left"},{"sibling":"282afa51266e47629e34d808a360bbb276348bcc5a24bdcc93e83a76e580293e","side":"right"},{"sibling":"05f89b32c00462e60adf95c1fe4579cdc2791b36e8b17573d8f3b5fd5da95a0b","side":"right"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_ad6d68c1c4570722c86c802aad90a495c36f181badf0b929dc6ed7ca8cfc1b64"}}