{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/property-directed-reachability-with-extended","title":"Property Directed Reachability with Extended Resolution","arxiv_id":"2505.18998","date":"2025-05-25","proceeding":null,"authors":["Andrew Luka","Yakir Vizel"],"abstract":"Property Directed Reachability (\\textsc{Pdr}), also known as IC3, is a state-of-the-art model checking algorithm widely used for verifying safety properties. While \\textsc{Pdr} is effective in finding inductive invariants, its underlying proof system, Resolution, limits its ability to construct short proofs for certain verification problems. This paper introduces \\textsc{PdrER}, a novel generalization of \\textsc{Pdr} that uses Extended Resolution (ER), a proof system exponentially stronger than Resolution, when constructing a proof of correctness. \\PdrEV leverages ER to construct shorter bounded proofs of correctness, enabling it to discover more compact inductive invariants. While \\PdrEV is based on \\textsc{Pdr}, it includes algorithmic enhancements that had to be made in order to efficiently use ER in the context of model checking. We implemented \\textsc{PdrER} in a new open-source verification framework and evaluated it on the Hardware Model Checking Competition benchmarks from 2019, 2020 and 2024. Our experimental evaluation demonstrates that \\textsc{PdrER} outperforms \\textsc{Pdr}, solving more instances in less time and uniquely solving problems that \\textsc{Pdr} cannot solve within a given time limit. We argue that this paper represents a significant step toward making strong proof systems practically usable in model checking.","url_abs":"https://arxiv.org/abs/2505.18998v1","url_pdf":"https://arxiv.org/pdf/2505.18998v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"property-directed-reachability-with-extended","repo_url":"https://github.com/technionfv/cav_2025_artifact","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}