{"paper":{"title":"Small Depth Proof Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andreas Krebs, Karteek Sreenivasaiah, Meena Mahajan, Nutan Limaye","submitted_at":"2013-07-18T10:31:44Z","abstract_excerpt":"A proof system for a language L is a function f such that Range(f) is exactly L. In this paper, we look at proofsystems from a circuit complexity point of view and study proof systems that are computationally very restricted. The restriction we study is: they can be computed by bounded fanin circuits of constant depth (NC^0), or of O(log log n) depth but with O(1) alternations (polylog AC^0). Each output bit depends on very few input bits; thus such proof systems correspond to a kind of local error-correction on a theorem-proof pair.\n  We identify exactly how much power we need for proof syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4897","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"}