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- W2952323281 abstract "Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a truth assignment satisfying $1-2^{-k}+p 2^{-k}$ of all clauses (observe that every $k$-CNF is 0-satisfiable). Also, let $F_k(n,m)$ denote a random $k$-CNF on $n$ variables formed by selecting uniformly and independently $m$ out of all possible $k$-clauses. It is easy to prove that for every $k>1$ and every $p$ in $(0,1]$, there is $R_k(p)$ such that if $r >R_k(p)$, then the probability that $F_k(n,rn)$ is $p$-satisfiable tends to 0 as $n$ tends to infinity. We prove that there exists a sequence $delta_k to 0$ such that if $r <(1-delta_k) R_k(p)$ then the probability that $F_k(n,rn)$is $p$-satisfiable tends to 1 as $n$ tends to infinity. The sequence $delta_k$ tends to 0 exponentially fast in $k$." @default.
- W2952323281 created "2019-06-27" @default.
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- W2952323281 date "2003-05-10" @default.
- W2952323281 modified "2023-09-27" @default.
- W2952323281 title "On the Maximum Satisfiability of Random Formulas" @default.
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