Average Time for the Full Pure Literal Rule

The simpliied pure literal algorithm solves satissability problems by c hoosing variables in a xed order and then generating subproblems for various values of the chosen variable. If some value satisses every relation that depends on the chosen variable, then only the subproblem for that preferred value is generated. Otherwise, a subproblem is generated for every value of the variable. The full pure literal algorithm chooses variables that have a preferred value before choosing those that do not. A recurrence equation is found for the average time used by the full pure literal rule algorithm when solving random conjunctive normal form satissability problems. The random problems are characterized by t h e n umber of variables v, the number of clauses t, and the probability that a literal is in a clause p. An asymptotic lower bound analysis shows that running time is more than polynomial in v when t increases more rapidly than ln v 2 when p is set to maximize the running time. A numerical study indicates that the results of the lower bound analysis are close to the true results. Thus, the full pure literal rule is faster than the simple pure literal rule where the polynomial time boundary occurs at t = ln v but slower than Franco's infrequent v ariable algorithm where the time is polynomial for all p when t = Ov 1=6 .