Satisfiability threshold for power law random 2-SAT in configuration model

We study Random 2-SAT problem, in which 2-CNFs are sampled from a wide range of non-uniform distributions, including heavy-tailed using random model that is quite different the standard uniform 2-SAT. This SAT so-called configuration model, given by distribution ξ for degree (or number occurrences) each variable. To generate formula variable , generating several clones Then 2-clauses created choosing partitioning into 2-element sets on set and assigning polarity literals at random. Here we consider problem power-law-like distributions . More precisely, assume such its right tail F ( x ) satisfies conditions W ℓ − α ≤ V some constants The main goal to satisfiability threshold phenomenon, show exists determined simple relation between first second moments