The Phase Transition Analysis for the Random Regular Exact 2-(d, k)-SAT Problem

In a regular (d,k)-CNF formula, each clause has length k and variable appears d times. A structure such as this is symmetric, the satisfiability problem of symmetric called (d,k)-SAT for short. The exact 2-(d,k)-SAT that formula F, if there truth assignment T, then exactly two literals in F are true. If contains only positive or negative literals, satisfiable T with size 2n/k 2-exactly satisfiable. This paper introduces instance generation model, constructs solution space, employs method first second moments to present phase transition point d* literals. When d<d*, can be satisfied high probability. d>d*, not Finally, verification results demonstrate theoretical consistent experimental results.