{"paper":{"title":"Which NP-Hard SAT and CSP Problems Admit Exponentially Improved Algorithms?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Magnus Wahlstr\\\"om, Victor Lagerkvist","submitted_at":"2018-01-29T13:06:44Z","abstract_excerpt":"We study the complexity of SAT($\\Gamma$) problems for potentially infinite languages $\\Gamma$ closed under variable negation (sign-symmetric languages). Via an algebraic connection, this reduces to the study of restricted partial polymorphisms of $\\Gamma$ we refer to as \\emph{pSDI-operations} (for partial, self-dual and idempotent). First, we study the language classes themselves. We classify the structure of the least restrictive pSDI-operations, corresponding to the most powerful languages $\\Gamma$, and find that these operations can be divided into \\emph{levels}, corresponding to a rough no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09488","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"}