{"paper":{"title":"Short Proofs for the Determinant Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Iddo Tzameret, Pavel Hrubes","submitted_at":"2011-12-29T10:18:16Z","abstract_excerpt":"We study arithmetic proof systems P_c(F) and P_f(F) operating with arithmetic circuits and arithmetic formulas, respectively, that prove polynomial identities over a field F. We establish a series of structural theorems about these proof systems, the main one stating that P_c(F) proofs can be balanced: if a polynomial identity of syntactic degree d and depth k has a P_c(F) proof of size s, then it also has a P_c(F) proof of size poly(s,d) and depth O(k+\\log^2 d + \\log d\\cd \\log s). As a corollary, we obtain a quasipolynomial simulation of P_c(F) by P_f(F), for identities of a polynomial syntac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6265","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"}