Tight Thresholds for The Pure Literal Rule
نویسنده
چکیده
We consider the threshold for the solvability of random k-SAT formulas (for k ≥ 3) using the pure literal rule. We demonstrate how this threshold can be found by using differential equations to determine the appropriate limiting behavior of the pure literal rule.
منابع مشابه
Structure of random r-SAT below the pure literal threshold
It is well known that there is a sharp density threshold for a random r-SAT formula to be satisfiable, and a similar, smaller, threshold for it to be satisfied by the pure literal rule. Also, above the satisfiability threshold, where a random formula is with high probability (whp) unsatisfiable, the unsatisfiability is whp due to a large “minimal unsatisfiable subformula” (MUF). By contrast, we...
متن کاملAn Exponential Lower Bound for the Pure Literal Rule
A pure literal is a literal in a logic formula (usually in Conjunctive Normal Form) that occurs only positively or only negatively. The Davis-Putnam Procedure [l] was developed to find one solution to a logic formula, and it contains several techniques for speeding up the typical solution time. One of these techniques is the pure literal rule: a variable that occurs only positively or only nega...
متن کاملAverage 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...
متن کاملTight Bounds For Random MAX 2-SAT
For a conjunctive normal form formula F with n variables and m = cn 2-variable clauses (c is called the density), denote by maxF is the maximum number of clauses satisfiable by a single assignment of the variables. For the uniform random formula F with density c = 1 + ε, ε À n−1/3, we prove that maxF is in (1 + ε−Θ(ε3))n with high probability. This improves the known upper bound (1 + ε − Ω(ε3/ ...
متن کاملExtended Failed-Literal Preprocessing for Quantified Boolean Formulas
ion makes Φ “truer” (more tree models). Pure existential literal rule makes Φ “falser” (fewer tree models). Pure universal literal rule makes Φ “falser” (fewer tree models). Unit-clause propagation and universal reduction do not change the set of tree models. So ? ? ? If abstraction changes u from universal to existential, and then it becomes pure, making it true is the wrong idea. Say u is ass...
متن کامل