The Local Cut Lemma

Lemma and Cut Strategies

Resolution has not been an eeective tool for deciding satissability of propositional CNF formulas, due to explosion of the search space, particularly when the formula is satissable. However, a new pruning method, which is designed to eliminate certain refutation attempts that cannot succeed, has been shown to eliminate much of the redundancy of propositional model elimination. The pruning metho...

Lemma and Cut Strategies for Propositional Model

This paper describes new \lemma" and \cut" strategies that are eecient to apply in the setting of propositional Model Elimination. It builds upon the C-literal strategy proposed by Shostak, and studied further by Letz, Mayr and Goller. Previous strategies for managing lemmas and C-literals in Model Elimination were oriented toward rst-order theorem proving. The original \cumulative" strategy re...

Constructive Lovasz Local Lemma

Let V be a finite set of independent random variables, and let A denote a finite set of events that are determined by V . That is, each event A ∈ A maps the set of assignments of V to {0, 1}. Definition 1. Given the set of independent random variables V and set of events A determined by the variables of V , define the relevant variables for an event A ∈ A, denoted vbl(A) ⊂ V to be the smallest ...

Lovász Local Lemma

Derandomizing the Lovasz Local Lemma more effectively

The famous Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove the existence of combinatorial objects meeting a prescribed collection of criteria. Kratochvil et al. applied this technique to prove that a k-CNF in which each variable appears at most 2^k/(ek) times is always satisfiable [KST93]. In a breakthrough paper, Beck found that if we lower the occurrences to O(2^(k/48...