Finding cores of random 2-SAT formulae via Poisson cloning

For the random 2-SAT formula F(n, p), let FC(n, p) be the formula left after the pure literal algorithm applied to F(n, p) stops. Using the recently developed Poisson cloning model together with the cut-off line algorithm (COLA), we completely analyze the structure of FC(n, p). In particular, it is shown that, for := p(2n - 1) = 1 + with n-1/3, the core of F(n, p) has 2 n + O(( n)1/2) variables and 2 n + O(( n))1/2 clauses, with high probability, where is the larger solution of the equation - (1 - e ) = 0. We also estimate the probability of F(n, p) being satisfiable to obtain Pr[F2(n, 2n-1 ) is satisfiable] = 1 - 1+o(1) 163n if = 1 - with n-1/3 e-(3n) if = 1 + with n-1/3, where o(1) goes to 0 as goes to 0. This improves the bounds of Bollob

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Jeong Han Kim
• Keywords: CORR 2008, Education, Poisson Cloning Model, Pure Literal Algorithm, Random 2-SAT Formula