{"paper":{"title":"Extended Resolution Clause Learning via Dual Implication Points","license":"http://creativecommons.org/licenses/by/4.0/","headline":"SAT solvers can learn stronger clauses by dynamically adding variables for dual implication points in the implication graph.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Albert Oliveras, Jonathan Chung, Sam Buss, Vijay Ganesh","submitted_at":"2024-06-20T10:50:26Z","abstract_excerpt":"We present a new extended resolution clause learning (ERCL) algorithm, implemented as part of a conflict-driven clause-learning (CDCL) SAT solver, wherein new variables are dynamically introduced as definitions for {\\it Dual Implication Points} (DIPs) in the implication graph constructed by the solver at runtime. DIPs are generalizations of unique implication points and can be informally viewed as a pair of dominator nodes, from the decision variable at the highest decision level to the conflict node, in an implication graph. We perform extensive experimental evaluation to establish the effica"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that xMapleLCM outperforms these solvers on Tseitin and XORified formulas.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Dynamically introducing new variables for DIPs at runtime produces net benefit without prohibitive overhead or compromising solver correctness on the evaluated instance classes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New ERCL method using dual implication points in CDCL solvers outperforms baselines on Tseitin and XORified formulas.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"SAT solvers can learn stronger clauses by dynamically adding variables for dual implication points in the implication graph.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"130704422065b1489782fd2501859f9d4653533a02a7b1a64b2694ee414c7a99"},"source":{"id":"2406.14190","kind":"arxiv","version":5},"verdict":{"id":"b838e7e6-0d26-4bc9-9681-2937b15edd73","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T00:27:27.539389Z","strongest_claim":"We show that xMapleLCM outperforms these solvers on Tseitin and XORified formulas.","one_line_summary":"New ERCL method using dual implication points in CDCL solvers outperforms baselines on Tseitin and XORified formulas.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Dynamically introducing new variables for DIPs at runtime produces net benefit without prohibitive overhead or compromising solver correctness on the evaluated instance classes.","pith_extraction_headline":"SAT solvers can learn stronger clauses by dynamically adding variables for dual implication points in the implication graph."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.14190/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}