{"paper":{"title":"The Renyi-Ulam pathological liar game with a fixed number of lies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Catherine H. Yan, Robert B. Ellis, Vadim Ponomarenko","submitted_at":"2004-07-28T23:15:34Z","abstract_excerpt":"The $q$-round Renyi-Ulam pathological liar game with $k$ lies on the set $[n]:=\\{1,...,n\\}$ is a 2-player perfect information zero sum game. In each round Paul chooses a subset $A\\subseteq [n]$ and Carole either assigns 1 lie to each element of $A$ or to each element of $[n]\\setminus A$. Paul wins if after $q$ rounds there is at least one element with $k$ or fewer lies. The game is dual to the original Renyi-Ulam liar game for which the winning condition is that at most one element has $k$ or fewer lies. We prove the existence of a winning strategy for Paul to the existence of a covering of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407504","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"}