{"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"}