The reachability problem for graphs cannot be described, in the sense of descriptive complexity theory, using a single first-order formula. This is true both for directed and undirected graphs, both in the finite and infinite. However, if we restrict ourselves to graphs in which a certain graph parameter is fixed ... more >>>

It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure theorems that characterize the exact expressive power of first-order logic with two variables on words. ... more >>>