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Planar Graph Isomorphism is in Log-Space
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. There is a significant gap between extantExpand
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An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas
We show here a 2<sup>Ω(√d·log N)</sup> size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N =Expand
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Lower bounds for depth 4 formulas computing iterated matrix multiplication
We study the arithmetic complexity of iterated matrix multiplication. We show that any multilinear homogeneous depth 4 arithmetic formula computing the product of <i>d</i> generic matrices of sizeExpand
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Longest Paths in Planar DAGs in Unambiguous Log-Space
Reachability and distance computation are known to be NL-complete in general graphs, but within UL ∩ co-UL if the graphs are planar. However, finding longest paths is known to be NP-complete, evenExpand
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The Coin Problem in Constant Depth: Sample Complexity and Parity Gates
The $\textit{\delta-Coin Problem}$ is the computational problem of distinguishing between coins that are heads with probability $(1+\delta)/2$ or $(1-\delta)/2,$ where $\delta$ is a parameter tendingExpand
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Upper Bounds for Monotone Planar Circuit Value and Variants
Abstract.The P-complete Circuit Value Problem CVP, when restricted to monotone planar circuits MPCVP, is known to be in NC3, and for the special case of upward stratified circuits, it is known to beExpand
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Planarity, Determinants, Permanents, and (Unique) Matchings
Viewing the computation of the determinant and the permanent of integer matrices as combinatorial problems on associated graphs, we explore the restrictiveness of planarity on their complexities andExpand
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Arithmetizing Classes Around NC 1 and L
The parallel complexity class NC1 has many equivalent models such as bounded width branching programs. Caussinus et.al[10] considered arithmetizations of two of these classes, #NC1 and #BWBP. WeExpand
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Streaming algorithms for language recognition problems
We study the complexity of the following problems in the streaming model. Membership testing forDLIN. We show that every language in DLIN can be recognized by a randomized one-pass O(logn) spaceExpand
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Evaluating Monotone Circuits on Cylinders, Planes and Tori
We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC3 in general, and in LogDCFL for the special case of upwardExpand
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