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- W1633286018 abstract "We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every clause has size exactly k. It was known that for k >= 3, Linear k-SAT is NP-complete if and only if an unsatisfiable linear k-CNF formula exists, and that they do exist for k >= 4. We prove that unsatisfiable linear k-CNF formulas exist for every k. Let f(k) be the minimum number of clauses in an unsatisfiable linear k-CNF formula. We show that f(k) is Omega(k2^k) and O(4^k*k^4), i.e., minimum size unsatisfiable linear k-CNF formulas are significantly larger than minimum size unsatisfiable k-CNF formulas. Finally, we prove that, surprisingly, linear k-CNF formulas do not allow for a larger fraction of clauses to be satisfied than general k-CNF formulas." @default.
- W1633286018 created "2016-06-24" @default.
- W1633286018 creator A5034846265 @default.
- W1633286018 date "2007-08-17" @default.
- W1633286018 modified "2023-09-27" @default.
- W1633286018 title "Unsatisfiable Linear k-CNFs Exist, for every k" @default.
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