Rejewski, Różycki, Zygalski lectures 2010

Date: friday, 28.05.2010, 11:00

Speaker: prof. Emo Welzl

Title: When Conflicting Constraints Can be Resolved - the Local Lemma and Satisfiability

Abstract: The general theme underlying the talk is the following question: Given a set of constraints, how much interleaving of these constraints (relative to how serious these constraints are) is necessary so that all of them cannot be satisfied simultaneously?

For a concrete setting we consider boolean formulas in conjunctive normal form (CNF), where the clauses play the role of constraints. If all clauses are large, it needs many clauses to obtain an unsatisfiable formula; moreover, these clauses have to interleave. We review quantitative results for the amount of interleaving required, many of which rely on the Lovász Local Lemma, a probabilistic lemma with many applications in combinatorics.

In positive terms, we are interested in simple combinatorial conditions which guarantee for a CNF formula to be satisfiable. The criteria obtained are nontrivial in the sense that even though they are easy to check, it is by far not obvious how to compute a satisfying assignment efficiently in case the conditions are fulfilled; until recently, it was not known how to do so. It is also remarkable that while deciding satisfiability is trivial for formulas that satisfy the conditions, a slightest relaxation of the conditions leads us into the territory of NP-completeness.

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Emo Welzl - a Profesor at Eidgenössische Technische Hochschule in Zurich (ETH); his research topics include, among others, computational geometry, optimalization of combinatorical models, geometrical structures analysis, discrete geometry, probabilistic methods and recently satisfiability; he was awarded the Max Planck Prize and the Gottfried Wilhelm Leibniz-Prize; member of Deutsche Akademie der Naturforscher Leopoldina.