2006/03/22 by Uriel Feige, Eran Ofek, E. O. Ofek +2
Computer Science · #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Rough Sets and Fuzzy Logic #cs.CC #cs.DS #cs.LO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.cs/0603084
14 pages
arxiv created 2006/03/22 · openalex publication_date 2006/03/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ϕ be a 3CNF formula with n variables and m clauses. A simple nonconstructive argument shows that when m is sufficiently large compared to n, most 3CNF formulas are not satisfiable. It is an open question whether there is an efficient refutation algorithm that for most such formulas proves that they are not satisfiable. A possible approach to refute a formula ϕ is: first, translate it into a graph Gϕ using a generic reduction from 3-SAT to max-IS, then bound the maximum independent set of Gϕ using the Lovasz ϑ function. If the ϑ function returns a value < m, this is a certificate for the unsatisfiability of ϕ. We show that for random formulas with m < n3/2 -o(1) clauses, the above approach fails, i.e. the ϑ function is likely to return a value of m.