{"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/community-based-3-sat-formulas-with-a","title":"Community-based 3-SAT Formulas with a Predefined Solution","arxiv_id":"1902.09706","date":"2019-02-26","proceeding":null,"authors":["Yamin Hu","Wenjian Luo","Junteng Wang"],"abstract":"It is crucial to generate crafted SAT formulas with predefined solutions for\nthe testing and development of SAT solvers since many SAT formulas from\nreal-world applications have solutions. Although some generating algorithms\nhave been proposed to generate SAT formulas with predefined solutions,\ncommunity structures of SAT formulas are not considered. We propose a 3-SAT\nformula generating algorithm that not only guarantees the existence of a\npredefined solution, but also simultaneously considers community structures and\nclause distributions. The proposed 3-SAT formula generating algorithm controls\nthe quality of community structures through controlling (1) the number of\nclauses whose variables have a common community, which we call intra-community\nclauses, and (2) the number of variables that only belong to one community,\nwhich we call intra-community variables. To study the combined effect of\ncommunity structures and clause distributions on the hardness of SAT formulas,\nwe measure solving runtimes of two solvers, gluHack (a leading CDCL solver) and\nCPSparrow (a leading SLS solver), on the generated SAT formulas under different\ngroups of parameter settings. Through extensive experiments, we obtain some\nnoteworthy observations on the SAT formulas generated by the proposed\nalgorithm: (1) The community structure has little or no effects on the hardness\nof SAT formulas with regard to CPSparrow but a strong effect with regard to\ngluHack. (2) Only when the proportion of true literals in a SAT formula in\nterms of the predefined solution is 0.5, SAT formulas are hard-to-solve with\nregard to gluHack; when this proportion is below 0.5, SAT formulas are\nhard-to-solve with regard to CPSparrow. (3) When the ratio of the number of\nclauses to that of variables is around 4.25, the SAT formulas are hard-to-solve\nwith regard to both gluHack and CPSparrow.","url_abs":"http://arxiv.org/abs/1902.09706v1","url_pdf":"http://arxiv.org/pdf/1902.09706v1.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":"abstracts"},"code_links":[{"paper_slug":"community-based-3-sat-formulas-with-a","repo_url":"https://github.com/YaminHuPaperCode/Community-based-SAT-Formulas","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}