The upper bound of phase transition point of multi literal satisfiability problem.

The satisfiability problem (SAT) refers to whether there is a set of boolean variable assignments that make at least one literal in each clause of the conjunctive normal form (CNF) formula true. The multi literal SAT problem refers to whether there is a set of boolean variable assignments that make at least two literals in each clause of the CNF formula true. Obviously, this problem is still an NP difficult problem. Defining as the ratio of the number of clauses in the CNF formula to the number of variables, we study the upper bound α* of phase transition point of the problem. If α strictly exceeds α*, the multi literal satisfaction problem is almost certainly unsatisfiable. A simple inference of the first moment can be used to prove α* =-ln 2/ln1-(k+1)/2k). α* =1 when k=3. The local maximum technique proposed by Kirousis et al is used to improve the upper bound α* of phase transition point of the multi literal 3-SAT problem to 0.719 3. Finally, a large amount of data is selected for experimental verification, and the results show that the theoretical results are consistent with the experimental results [ABSTRACT FROM AUTHOR]