Modeling tiling problems as SAT problems I read that tiling problems can be modeled as satisfiability problems (2-SAT?), but the author did not explain how. Is this true? What would be an example?

By a "tiling problem" I mean you have a matrix and have to fill it up according to some constraint. For example, you might have to fill the matrix with a particular shape, or the values in the matrix have to adhere to some constraint. For example, imagine a partially filled matrix and the rule is that you have to fill it with values that are one more or one less than the adjoining values, or something like that.
One example of a tiling problem that was successfully attacked by reducing it to a SAT instance was rectangular grid coloring.  In "Extremely Complex 4-Colored Rectangle-Free Grids:
Solution of Open Multiple-Valued Problems" the authors describe how they tackled 17x17, 17x18, and 18x18 grid colorings using a SAT solver plus some previous knowledge of grid coloring theory to pare down the search space.