Abstract

In this talk, I shall discuss and connect some of the main ideas surrounding the vast and interesting topic of Boolean CNF Satisfiability. The motivation shall be the possible development of new insights or algorithms, or an understanding of why some algorithms for SAT might or might not work better than others. I shall start with the above graph but without any edges, and go on to fill in all the edges of the graph through the talk, in near anticlockwise order from the bottom (if there is shortage of time, I will not talk about the two player pebble games, and if there is even less time then I’ll just gloss over proof complexity).

some keywords:

AI – logic + probability, CNF -SAT, belief propagation, threshold phenomena, factor graphs, survey propagation, integer programming, LP relaxations, convergent message passing, dual decomposition, clause driven conflict learning, resolution, extended resolution, marginal polytope, convex hulls, cutting planes, chvatal-gomory, sherali-adams, lovasz-schrijver, lasserre, proof systems, size/width/rank/space of proofs, etc