Matching is as easy as matrix inversion
Combinatorica
Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
The method of forced enumeration for nondeterministic automata
Acta Informatica
Nondeterministic space is closed under complementation
SIAM Journal on Computing
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
Counting quantifiers, successor relations, and logarithmic space
Journal of Computer and System Sciences - special issue on complexity theory
Isolation, matching and counting uniform and nonuniform upper bounds
Journal of Computer and System Sciences
Making Nondeterminism Unambiguous
SIAM Journal on Computing
An Unambiguous Class Possessing a Complete Set
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Searching Constant Width Mazes Captures the AC0 Hierarchy
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On Representations of Some Thickness-Two Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
Unambiguity and Fewness for Logarithmic Space
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
The complexity of planarity testing
Information and Computation
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Grid Graph Reachability Problems
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
On the power of the compass (or, why mazes are easier to search than graphs)
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Longest paths in planar DAGs in unambiguous logspace
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
The directed planar reachability problem
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Planarity, determinants, permanents, and (unique) matchings
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Logspace Reduction of Directed Reachability for Bounded Genus Graphs to the Planar Case
ACM Transactions on Computation Theory (TOCT)
Planarity, Determinants, Permanents, and (Unique) Matchings
ACM Transactions on Computation Theory (TOCT)
On the Power of Isolation in Planar Graphs
ACM Transactions on Computation Theory (TOCT)
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Space complexity of perfect matching in bounded genus bipartite graphs
Journal of Computer and System Sciences
Green's theorem and isolation in planar graphs
Information and Computation
Grid graphs with diagonal edges and the complexity of xmas mazes
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Computational Complexity
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We make progress in understanding the complexity of the graph reachability problem in the context of unambiguous logarithmic space computation; a restricted form of nondeterminism. As our main result, we show a new upper bound on the directed planar reachability problem by showing that it can be decided in the class unambiguous logarithmic space (UL). We explore the possibility of showing the same upper bound for the general graph reachability problem. We give a simple reduction showing that the reachability problem for directed graphs with thickness two is complete for the class nondeterministic logarithmic space (NL). Hence an extension of our results to directed graphs with thickness two will unconditionally collapse NL to UL.