{"type":"ScholarlyArticle","title":"Weighted, Circular and Semi-Algebraic Proofs (Abstract Reprint)","authors":[{"name":"Ilario Bonacina","slug":"ilario-bonacina","given":"Ilario","family":"Bonacina","affiliation":"UPC Universitat Politecnica de Catalunya"},{"name":"Maria Luisa Bonet","slug":"maria-luisa-bonet","given":"Maria Luisa","family":"Bonet","affiliation":"UPC Universitat Politecnica de Catalunya"},{"name":"Jordi Levy","slug":"jordi-levy","given":"Jordi","family":"Levy","affiliation":"Artificial Intelligence Research Institute (IIIA)"}],"abstract":"In recent years there has been an increasing interest in studying proof systems stronger than Resolution, with the aim of building more efficient SAT solvers based on them. In defining these proof systems, we try to find a balance between the power of the proof system (the size of the proofs required to refute a formula) and the difficulty of finding the proofs.\r\n\r\nIn this paper we consider the proof systems circular Resolution, Sherali-Adams, Nullstellensatz and Weighted Resolution and we study their relative power from a theoretical perspective. We prove that circular Resolution, Sherali-Adams and Weighted Resolution are polynomially equivalent proof systems. We also prove that Nullstellensatz is polynomially equivalent to a restricted version of Weighted Resolution. The equivalences carry on also for versions of the systems where the coefficients/weights are expressed in unary.\r\n\r\nThe practical interest in these systems comes from the fact that they admit efficient algorithms to find proofs in case these have small width/degree.","doi":"10.24963/ijcai.2024/947","url":"https://ijcai.org/proceedings/2024/947","pdf":"https://ijcai.org/proceedings/2024/0947.pdf","markdown":"https://ijcai.org/proceedings/2024/947.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/947","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Journal Track","track":"Journal Track","number":947,"pages":{"first":8475,"last":8475},"keywords":["Journal Track: Journal Track"],"videos":[],"references":[{"position":1,"raw":"[Bonacina et al., 2024] Ilario Bonacina, Maria Luisa Bonet, and Jordi Levy. Weighted, circular and semi-algebraic proofs. J. Artif. Intell. Res., 79:447-482, 2024.","title":"Weighted, circular and semi-algebraic proofs","authors":"Ilario Bonacina, Maria Luisa Bonet, Jordi Levy","year":"2024","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}