{"paper":{"title":"Some Results on Circuit Lower Bounds and Derandomization of Arthur-Merlin Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"D. M. Stull","submitted_at":"2017-01-16T19:20:42Z","abstract_excerpt":"We prove a downward separation for $\\mathsf{\\Sigma}_2$-time classes. Specifically, we prove that if $\\Sigma_2$E does not have polynomial size non-deterministic circuits, then $\\Sigma_2$SubEXP does not have \\textit{fixed} polynomial size non-deterministic circuits. To achieve this result, we use Santhanam's technique on augmented Arthur-Merlin protocols defined by Aydinlio\\u{g}lu and van Melkebeek. We show that augmented Arthur-Merlin protocols with one bit of advice do not have fixed polynomial size non-deterministic circuits. We also prove a weak unconditional derandomization of a certain typ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04428","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"}