{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:ACXKPI77LWBLNNZHDP7DTRI7EJ","short_pith_number":"pith:ACXKPI77","schema_version":"1.0","canonical_sha256":"00aea7a3ff5d82b6b7271bfe39c51f224794d28531fa0bb8ff9d7ce50a7e6c0c","source":{"kind":"arxiv","id":"1904.11573","version":2},"attestation_state":"computed","paper":{"title":"B\\\"uchi Objectives in Countable MDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.OC"],"primary_cat":"math.PR","authors_text":"Mahsa Shirmohammadi, Patrick Totzke, Richard Mayr, Stefan Kiefer","submitted_at":"2019-04-25T20:29:11Z","abstract_excerpt":"We study countably infinite Markov decision processes with B\\\"uchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill in 1979 is whether there always exist $\\varepsilon$-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so far. We provide a negative answer to this question by constructing a non-trivial counterexample. On the other hand, we show that Markov strategies with only 1 bit of extra memory are sufficient."},"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":"1904.11573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T20:29:11Z","cross_cats_sorted":["cs.FL","math.OC"],"title_canon_sha256":"feea2995072c3549fcec2d596f960231c4e2b3927d0ae011a340ef0da8f53214","abstract_canon_sha256":"2c8de089e03b790df995b7cd7908d261827d8d2050aaf1c6cda303027df73681"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:24.676211Z","signature_b64":"dQUgav+GsV1CXuTTNRkGQHabDOITpgSX1fcv5ZGBhO9cWZiiy7Li31u8ZyJdF1bc+TYnBYRR1V79LYrglBOeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00aea7a3ff5d82b6b7271bfe39c51f224794d28531fa0bb8ff9d7ce50a7e6c0c","last_reissued_at":"2026-05-17T23:47:24.675665Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:24.675665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"B\\\"uchi Objectives in Countable MDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.OC"],"primary_cat":"math.PR","authors_text":"Mahsa Shirmohammadi, Patrick Totzke, Richard Mayr, Stefan Kiefer","submitted_at":"2019-04-25T20:29:11Z","abstract_excerpt":"We study countably infinite Markov decision processes with B\\\"uchi objectives, which ask to visit a given subset of states infinitely often. A question left open by T.P. Hill in 1979 is whether there always exist $\\varepsilon$-optimal Markov strategies, i.e., strategies that base decisions only on the current state and the number of steps taken so far. We provide a negative answer to this question by constructing a non-trivial counterexample. On the other hand, we show that Markov strategies with only 1 bit of extra memory are sufficient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11573","kind":"arxiv","version":2},"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":"1904.11573","created_at":"2026-05-17T23:47:24.675765+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.11573v2","created_at":"2026-05-17T23:47:24.675765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11573","created_at":"2026-05-17T23:47:24.675765+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACXKPI77LWBL","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACXKPI77LWBLNNZH","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACXKPI77","created_at":"2026-05-18T12:33:12.712433+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/ACXKPI77LWBLNNZHDP7DTRI7EJ","json":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ.json","graph_json":"https://pith.science/api/pith-number/ACXKPI77LWBLNNZHDP7DTRI7EJ/graph.json","events_json":"https://pith.science/api/pith-number/ACXKPI77LWBLNNZHDP7DTRI7EJ/events.json","paper":"https://pith.science/paper/ACXKPI77"},"agent_actions":{"view_html":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ","download_json":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ.json","view_paper":"https://pith.science/paper/ACXKPI77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.11573&json=true","fetch_graph":"https://pith.science/api/pith-number/ACXKPI77LWBLNNZHDP7DTRI7EJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ACXKPI77LWBLNNZHDP7DTRI7EJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ/action/storage_attestation","attest_author":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ/action/author_attestation","sign_citation":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ/action/citation_signature","submit_replication":"https://pith.science/pith/ACXKPI77LWBLNNZHDP7DTRI7EJ/action/replication_record"}},"created_at":"2026-05-17T23:47:24.675765+00:00","updated_at":"2026-05-17T23:47:24.675765+00:00"}