{"paper":{"title":"A Satisfiability Algorithm for AC$^0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Ramamohan Paturi, Russell Impagliazzo, William Matthews","submitted_at":"2011-07-15T18:37:49Z","abstract_excerpt":"We consider the problem of efficiently enumerating the satisfying assignments to $\\AC^0$ circuits. We give a zero-error randomized algorithm which takes an $\\AC^0$ circuit as input and constructs a set of restrictions which partition $\\{0,1\\}^n$ so that under each restriction the value of the circuit is constant. Let $d$ denote the depth of the circuit and $cn$ denote the number of gates. This algorithm runs in time $|C| 2^{n(1-\\mu_{c.d})}$ where $|C|$ is the size of the circuit for $\\mu_{c,d} \\ge 1/\\bigO[\\lg c + d \\lg d]^{d-1}$ with probability at least $1-2^{-n}$.\n  As a result, we get impro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3127","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"}