A Novel Method for Counting Models on Grid Boolean Formulas

Abstract

We research on the possible orientations patterns of a grid graph G, and propose a method for counting certain combinatorial structures over the class of orientations of G. For example, our method can be applied for counting sink-free orientations of G, as well as it can be applied for solving the #2SAT problem for grid Boolean formulas. Our proposal extends the classical transfer matrix method used for counting the number of independent sets in a grid.