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Directed planar reachability is in unambiguous logspace
 In Proceedings of IEEE Conference on Computational Complexity CCC
, 2007
"... We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1. ..."
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We show that the stconnectivity problem for directed planar graphs can be decided in unambiguous logarithmic space. 1.
The directed planar reachability problem
 In Proc. 25th annual Conference on Foundations of Software Technology and Theoretical Computer Science (FST&TCS), number 1373 in Lecture Notes in Computer Science
, 2005
"... Abstract. We investigate the stconnectivity 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 logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the ..."
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Cited by 23 (9 self)
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Abstract. We investigate the stconnectivity 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 logspacereducible to its complement, and we show that the problem of searching graphs of genus 1 reduces to the planar case. We also consider a previouslystudied subclass of planar graphs known as grid graphs. We show that the directed planar stconnectivity problem reduces to the reachability problem for directed grid graphs. A special case of the gridgraph reachability problem where no edges are directed from right to left is known as the “acyclic grid graph reachability problem”. We show that this problem lies in the complexity class UL. 1
On Monotone Planar Circuits
, 1999
"... In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in nonuniform AC 0 . This provides a striking contrast to the nonplanar case, where exactly NC 1 i ..."
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Cited by 19 (2 self)
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In this paper we show several results about monotone planar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables, compute exactly the functions in nonuniform AC 0 . This provides a striking contrast to the nonplanar case, where exactly NC 1 is computed. We show that the circuit value problem for monotone planar circuits, with inputs on the outer face only, can be solved in LOGDCFL ` SC, improving a LOGCFL upper bound due to Dymond and Cook. We show that for monotone planar circuits, with inputs on the outer face only, excessive depth compared to width is useless; any function computed by a monotone planar circuit of width w with inputs on the outer face can be computed by a monotone planar circuit of width O(w) and depth w O(1) . Finally, we show that monotone planar readonce circuits, with inputs on the outer face only, can be efficiently learned using membership queries. 1 Introduction In this paper, we prove a number of ...
Word problems and membership problems on compressed words
 SIAM J. Comput., 35(5):1210
"... Abstract. We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid M, and we ask whether these two words represent the same monoid element of M. Words are compressed using str ..."
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Abstract. We consider a compressed form of the word problem for finitely presented monoids, where the input consists of two compressed representations of words over the generators of a monoid M, and we ask whether these two words represent the same monoid element of M. Words are compressed using straightline programs, i.e., contextfree grammars that generate exactly one word. For several classes of finitely presented monoids we obtain completeness results for complexity classes in the range from P to EXPSPACE. As a byproduct of our results on compressed word problems we obtain a fixed deterministic contextfree language with a PSPACEcomplete compressed membership problem. The existence of such a language was open so far. Finally, we will investigate the complexity of the compressed membership problem for various circuit complexity classes. Key words. grammarbased compression, word problems for monoids, contextfree languages, complexity AMS subject classifications. 20F10, 68Q17, 68Q42
Grid Graph Reachability Problems
 IN ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY
, 2006
"... We study the complexity of restricted versions of stconnectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since • reachability on grid graphs is logspaceequivalent to reachability in general planar digraphs, and • reachability on certain classes o ..."
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Cited by 14 (9 self)
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We study the complexity of restricted versions of stconnectivity, which is the standard complete problem for NL. Grid graphs are a useful tool in this regard, since • reachability on grid graphs is logspaceequivalent to reachability in general planar digraphs, and • reachability on certain classes of grid graphs gives natural examples of problems that are hard for NC 1 under AC 0 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 connectivity can be solved in logspace, by building on the work of Jakoby et al. [11], who showed that reachability in seriesparallel digraphs is solvable in L. Our main results are: • Many of the natural restrictions on gridgraph reachability (GGR) are equivalent under AC 0
Polynomialsize Frege and Resolution Proofs of stConnectivity and Hex Tautologies
 Theorectical Computer Science
, 2003
"... A grid graph has rectangularly arranged vertices with edges permitted only between orthogonally adjacent vertices. The stconnectivity principle states that it is not possible to have a red path of edges and a green path of edges which connect diagonally opposite corners of the grid graph unless ..."
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A grid graph has rectangularly arranged vertices with edges permitted only between orthogonally adjacent vertices. The stconnectivity principle states that it is not possible to have a red path of edges and a green path of edges which connect diagonally opposite corners of the grid graph unless the paths cross somewhere.
Bounded Depth Arithmetic Circuits: Counting and Closure
, 1999
"... Constantdepth arithmetic circuits have been defined and studied in [AAD97, ABL98]; these circuits yield the function classes #AC . These function classes in turn provide new characterizations of the computational power of threshold circuits, and provide a link between the circuit classes AC ..."
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Constantdepth arithmetic circuits have been defined and studied in [AAD97, ABL98]; these circuits yield the function classes #AC . These function classes in turn provide new characterizations of the computational power of threshold circuits, and provide a link between the circuit classes AC (where many lower bounds are known) and TC (where essentially no lower bounds are known). In this paper, we resolve several questions regarding the closure properties of #AC .
New Lower Bound Techniques For Dynamic Partial Sums and Related Problems
 SIAM Journal on Computing
, 2003
"... We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kin ..."
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We study the complexity of the dynamic partial sum problem in the cellprobe model. We give the model access to nondeterministic queries and prove that the problem remains hard. We give the model access to the right answer as an oracle and prove that the problem remains hard. This suggests which kind of information is hard to maintain. From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs, planarity testing, planar point location, incremental parsing, and fundamental data structure problems like maintaining the majority of the prefixes of a string of bits. We prove a lower bound for reachability in grid graphs in terms of the graph's width. We characterize the complexity of maintaining the value of any symmetric function on the prefixes of a bit string. Keywords. cellprobe model, partial sum, dynamic algorithm, data structure AMS subject classifications. 68Q17, 68Q10, 68Q05, 68P05
Circuits on Cylinders
, 2002
"... We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a #2 circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (o ..."
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We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a #2 circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC .
Oneinputface MPCVP is Hard for L, but in LogDCFL
"... A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that ev ..."
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Cited by 9 (3 self)
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A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the oneinputface MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted oneinputface MPCVP is also in LogDCFL. We also show this problem to be Lhard under quantifier free projections.