{"paper":{"title":"On Restricting No-Junta Boolean Function and Degree Lower Bounds by Polynomial Method","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chia-Jung Lee, Ming-Chuan Yang, Satya V. Lokam, Shi-Chun Tsai","submitted_at":"2015-02-02T04:45:21Z","abstract_excerpt":"Let $\\mathcal{F}_{n}^*$ be the set of Boolean functions depending on all $n$ variables. We prove that for any $f\\in \\mathcal{F}_{n}^*$, $f|_{x_i=0}$ or $f|_{x_i=1}$ depends on the remaining $n-1$ variables, for some variable $x_i$. This existent result suggests a possible way to deal with general Boolean functions via its subfunctions of some restrictions.\n  As an application, we consider the degree lower bound of representing polynomials over finite rings. Let $f\\in \\mathcal{F}_{n}^*$ and denote the exact representing degree over the ring $\\mathbb{Z}_m$ (with the integer $m>2$) as $d_m(f)$. L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00357","kind":"arxiv","version":2},"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"}