{"paper":{"title":"Tighter Hard Instances for PPSZ","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dominik Scheder, Navid Talebanfard, Pavel Pudl\\'ak","submitted_at":"2016-11-04T09:27:34Z","abstract_excerpt":"We construct uniquely satisfiable $k$-CNF formulas that are hard for the algorithm PPSZ. Firstly, we construct graph-instances on which \"weak PPSZ\" has savings of at most $(2 + \\epsilon) / k$; the saving of an algorithm on an input formula with $n$ variables is the largest $\\gamma$ such that the algorithm succeeds (i.e. finds a satisfying assignment) with probability at least $2^{ - (1 - \\gamma) n}$. Since PPSZ (both weak and strong) is known to have savings of at least $\\frac{\\pi^2 + o(1)}{6k}$, this is optimal up to the constant factor. In particular, for $k=3$, our upper bound is $2^{0.333\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01291","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"}