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On finite decomposition complexity of Thompson's group F
Thompson's group F Finite decomposition complexity Word-metric Exact metric spaces Reduced forest diagram
2011/10/20
Finite decomposition complexity m(FDC) is a large scale property of a metricspace. It generalizes finite asymptoticdimension and applies to a wide class of groups. To make the property quantitative, a...
The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems
Streaming Complexity Cycle Counting,
2012/12/3
In this paper we introduce a new technique for proving streaming lower bounds (and one-way communication lower bounds), by reductions from a problem called the Boolean Hidden Hypermatching problem (BH...
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in p 2 . In the case of linear matroids, which are
represented over polynomially growing fie...
Average-Case Separation in Proof Complexity:Short Propositional Refutations for Random 3CNF Formulas
Average-Case Short Propositional Random 3CNF Formulas
2012/12/4
Separating different propositional proof systems梩hat is, demonstrating that one proof system cannot efficiently simulate another proof system梚s one of the main goals of proof complexity. Nevertheless,...
Complexity of Total {k}-Domination and Related Problems
Complexity Total {k}-Domination Problems
2012/12/3
In this paper, we study the {k}-domination, total {k}-domination, {k}-domatic number, and total {k}-domatic number problems, from complexity and algorithmic points of view. Let k ∶ 1 be a fixed intege...
Randomized Communication Complexity for Linear Algebra Problems over Finite Fields
communication complexity streaming, matrix singularity determinant
2012/12/3
Finding the singularity of a matrix is a basic problem in linear algebra. Chu and Schnitger first considered this problem in the communication complexity model, in which Alice holds the first half of ...
Algorithmic and Complexity Results for Cutting Planes Derived from Maximal Lattice-Free Convex Sets
Algorithmic and Complexity Results Maximal Lattice-Free Convex Sets Optimization and Control
2011/9/20
Abstract: We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Anderse...
On abelian and additive complexity in infinite words
additive complexity infinite words Combinatorics
2011/9/19
Abstract: The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity f...
Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity
SNR-gap subexponential complexity Information Theory
2011/9/15
Abstract: The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-p...
A Computational Complexity-Theoretic Elaboration of Weak Truth-Table Reducibility
algorithmic information theory algorithmic randomness weak truth-table reducibility
2011/9/14
Abstract: The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use functi...
On the computational complexity of stochastic controller optimization in POMDPs
Partially observable Markov decision process stochastic controller bilinear program computational complexity Motzkin-Straus theorem
2011/10/8
Abstract: We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and...
Iteration Complexity of Randomized Block-Coordinate Descent Methods for Minimizing a Composite Function
Block coordinate descent iteration complexity composite minimization coordinate relaxation alternating minimization
2011/9/6
Abstract: In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $...
Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)
Complexity the Classical Lie Superalgebra gl(m|n) Representation Theory
2011/9/5
Abstract: Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules whi...
Linear Complexity Lossy Compressor for Binary Redundant Memoryless Sources
nonlinear function LDGM codes lossy compression replica method
2011/8/30
Abstract: A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryl...
The entropy functional, the information path functional's essentials and their connections to Kolmogorov's entropy, complexity and physics
Additive functional Entropy Singularities Natural Border Problem Invariant
2011/8/31
Abstract: The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, and the information path functional (IPF), analyzing their connect...