Polynomial-average-time satisfiability problems (Q1095678)

Let p(v) be the probability for any of 2v literals (formed from v variables) to appear in a clause, t(v) be the number of clauses in a random predicate. The average time for determining satisfiability using backtracking is investigated. It takes polynomial average time if lim vp(v)\(=0\), t(v)\(\geq (\ln 2+\epsilon)v/(-\ln ((v+1)p(v)))\) or if lim vp(v)\(=\infty\), lim p(v)\(=0\), t(v)\(\geq ((\ln 2+\epsilon)/\exp (v))\exp (2vp(v))\); the intermediate cases are also covered.