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Summary: Grid Graph Reachability Problems
Eric Allender
David A. Mix Barrington
Tanmoy Chakraborty
Samir Datta§
Sambuddha Roy¶
Abstract
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
natural examples of problems that are hard for NC1
under AC0
reductions but are not known to be hard for
L; they thus give insight into the structure of L.
In addition to explicating the structure of L, another of our
goals is to expand the class of digraphs for which connec-
tivity can be solved in logspace, by building on the work of
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