{"paper":{"title":"Tree-like resolution complexity of two planar problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anna Malova, Dmitry Itsykson, Dmitry Sokolov, Vsevolod Oparin","submitted_at":"2014-12-02T22:37:17Z","abstract_excerpt":"We consider two CSP problems: the first CSP encodes 2D Sperner's lemma for the standard triangulation of the right triangle on $n^2$ small triangles; the second CSP encodes the fact that it is impossible to match cells of $n \\times n$ square to arrows (two horizontal, two vertical and four diagonal) such that arrows in two cells with a common edge differ by at most $45^\\circ$, and all arrows on the boundary of the square do not look outside (this fact is a corollary of the Brower's fixed point theorem). We prove that the tree-like resolution complexities of these CSPs are $2^{\\Theta(n)}$. For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1124","kind":"arxiv","version":1},"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"}