{"paper":{"title":"Certificate-Aware Property-Directed Reachability","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A certificate-aware variant of property-directed reachability jointly optimizes runtime, certificate size, and checker time on hardware safety problems.","cross_cats":["cs.AR"],"primary_cat":"cs.LO","authors_text":"Arman Ferdowsi, Laura Kovacs","submitted_at":"2026-05-15T14:15:33Z","abstract_excerpt":"Property-Directed Reachability (PDR/IC3) is a standard workhorse for hardware safety verification, but most implementations are tuned primarily for time-to-answer and treat the produced invariant or counterexample as a secondary byproduct. In certified workflows, including recent hardware model checking competition rules, the certificate becomes a deliverable whose size, independent checking time, and reproducibility directly affect end-to-end cost.\n  We present CAPDR, a certificate-aware variant of PDR that targets a joint objective over runtime, certificate size, and checker time, while keep"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On the 2024 Hardware Model Checking Competition bit-level safety benchmarks, CAPDR solves six more instances than the baseline. Over each configuration's checker-accepted solved set, the median certificate-size proxy decreases by 24.6% and the median checker time by 49%. Post-fixpoint invariant minimization yields further reductions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The learned ranking policy over PDR choice points (blocker generalization, obligation ordering, clause pushing) produces the observed joint improvements without introducing any unsoundness, given that every state-changing action remains guarded by the identical SAT checks as standard PDR and final claims are accepted only after independent checker validation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CAPDR augments PDR with a learned ranking policy over blocker generalization, obligation ordering, and clause pushing to reduce median certificate size by 24.6% and checker time by 49% while solving six additional 2024 HWMCC bit-level safety instances.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A certificate-aware variant of property-directed reachability jointly optimizes runtime, certificate size, and checker time on hardware safety problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c43c3a13fb9e5dceb8986c96c6426a80497cc198f9e41450c493d025ff5c093e"},"source":{"id":"2605.16472","kind":"arxiv","version":1},"verdict":{"id":"c9d66d38-d9da-4fd4-8134-a0de9d19f16d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:44:28.954707Z","strongest_claim":"On the 2024 Hardware Model Checking Competition bit-level safety benchmarks, CAPDR solves six more instances than the baseline. Over each configuration's checker-accepted solved set, the median certificate-size proxy decreases by 24.6% and the median checker time by 49%. Post-fixpoint invariant minimization yields further reductions.","one_line_summary":"CAPDR augments PDR with a learned ranking policy over blocker generalization, obligation ordering, and clause pushing to reduce median certificate size by 24.6% and checker time by 49% while solving six additional 2024 HWMCC bit-level safety instances.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The learned ranking policy over PDR choice points (blocker generalization, obligation ordering, clause pushing) produces the observed joint improvements without introducing any unsoundness, given that every state-changing action remains guarded by the identical SAT checks as standard PDR and final claims are accepted only after independent checker validation.","pith_extraction_headline":"A certificate-aware variant of property-directed reachability jointly optimizes runtime, certificate size, and checker time on hardware safety problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16472/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:23.282438Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:52:01.992668Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:23.116098Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:57.050155Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4635829a231a8ade815a783f6ff80cf3675475ebf806b56eb0651d4487b048d5"},"references":{"count":34,"sample":[{"doi":"","year":2011,"title":"Sat-based model checking without unrolling,","work_id":"a95c4290-1123-41e3-b7a8-2068b5c3f85a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Introducing certificates to the hardware model checking competition,","work_id":"a79ad8fa-0216-46cb-9d05-25130586c514","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Hardware model checking competition 2025,","work_id":"c83d9fa9-340f-481a-a537-a58e210f2268","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Improvements in software verification and witness validation: SV-COMP 2025,","work_id":"f7397fdd-b0d1-434e-9a94-33e2507d6ed8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Deepic3: Guiding ic3 algorithms by graph neural network clause prediction,","work_id":"7b21f59e-9cb1-44f7-8775-54ce87bf9903","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":34,"snapshot_sha256":"70fd83198265bf1ec5647a3f5ca1cffd0b1e8bb389e5d750447a5a11d33362d1","internal_anchors":1},"formal_canon":{"evidence_count":1,"snapshot_sha256":"99c24a8b5b67cc8c90c0d7645cc66d27796f895d4ad82070bb77c8a72106adb3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}