We show that searching a width k maze is complete for \Pi_k, i.e., for the k'th level of the AC^0 hierarchy. Equivalently, st-connectivity for width k grid graphs is complete for \Pi_k. As an application, we show that there is a data structure solving dynamic st-connectivity for constant width grid ... more >>>

We investigate the s-t-connectivity problem for directed planar graphs, which is hard for L and is contained in NL but is not known to be complete. We show that this problem is logspace-reducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to ... more >>>

We study the complexity of restricted versions of st-connectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since * reachability on grid graphs is logspace-equivalent to reachability in general planar digraphs, and * reachability on certain classes of grid graphs gives ... more >>>