{"paper":{"title":"Extending CDCL to disjunctions of parity equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.LO","authors_text":"Glenn Sun, Paul Beame","submitted_at":"2026-05-14T16:05:13Z","abstract_excerpt":"Because CDCL produces proofs in the Resolution proof system, problems provably hard for Resolution are also provably hard for CDCL. Exponentially shorter proofs can sometimes be found using stronger proof systems such as $\\text{Res}(\\oplus)$, a generalization of Resolution to XNF formulas, whose constraints are disjunctions of parity equations (\"linear clauses\") such as $(x \\oplus y) \\lor \\lnot (y \\oplus z)$. While some modern solvers like CryptoMiniSAT reason on Boolean clauses with separate parity equations, reasoning about more general linear clauses is less explored.\n  We present $\\text{CD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15002","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"}