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Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…

Quantum Physics · Physics 2024-10-08 Debajyoti Bera , Tharrmashastha SAPV

In this paper, we study the structure of set-multilinear arithmetic circuits and set-multilinear branching programs with the aim of showing lower bound results. We define some natural restrictions of these models for which we are able to…

Computational Complexity · Computer Science 2015-11-10 V. Arvind , S. Raja

Evolutionary algorithms (EAs) are population-based general-purpose optimization algorithms, and have been successfully applied in various real-world optimization tasks. However, previous theoretical studies often employ EAs with only a…

Neural and Evolutionary Computing · Computer Science 2016-06-13 Chao Qian , Yang Yu , Zhi-Hua Zhou

It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of…

Quantum Physics · Physics 2013-03-26 Andris Ambainis , Ronald de Wolf

We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…

Data Structures and Algorithms · Computer Science 2016-05-03 Sariel Har-Peled , Piotr Indyk , Sepideh Mahabadi , Ali Vakilian

Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field…

Computational Complexity · Computer Science 2009-09-29 Jakob Nordström , Johan Håstad

Arrangements of pseudolines are classic objects in discrete and computational geometry. They have been studied with increasing intensity since their introduction almost 100 years ago. The study of the number $B_n$ of non-isomorphic simple…

Combinatorics · Mathematics 2024-03-22 Fernando Cortés Kühnast , Justin Dallant , Stefan Felsner , Manfred Scheucher

We study local symmetry breaking problems in the CONGEST model, focusing on ruling set problems, which generalize the fundamental Maximal Independent Set (MIS) problem. A $\beta$-ruling set is an independent set such that every node in the…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-05-25 Shreyas Pai , Gopal Pandurangan , Sriram V. Pemmaraju , Talal Riaz , Peter Robinson

Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…

Computational Complexity · Computer Science 2008-05-15 Alexander A. Sherstov

We consider the dictionary problem in external memory and improve the update time of the well-known buffer tree by roughly a logarithmic factor. For any \lambda >= max {lg lg n, log_{M/B} (n/B)}, we can support updates in time O(\lambda /…

Data Structures and Algorithms · Computer Science 2011-04-15 John Iacono , Mihai Pǎtraşcu

We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…

Dynamical Systems · Mathematics 2026-01-15 Samuel Everett

Recent works explore deep learning's success by examining functions or data with hierarchical structure. To study the learning complexity of functions with hierarchical structure, we study the noise stability of functions with tree…

Probability · Mathematics 2025-09-30 Rupert Li , Elchanan Mossel

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via linear programs (LPs), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend…

Computational Complexity · Computer Science 2016-10-26 Gábor Braun , Samuel Fiorini , Sebastian Pokutta

Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this…

Statistics Theory · Mathematics 2023-10-31 Sinho Chewi , Jaume de Dios Pont , Jerry Li , Chen Lu , Shyam Narayanan

Technology trends will cause data movement to account for the majority of energy expenditure and execution time on emerging computers. Therefore, computational complexity will no longer be a sufficient metric for comparing algorithms, and a…

Computational Complexity · Computer Science 2014-11-11 Venmugil Elango , Fabrice Rastello , Louis-Noel Pouchet , J. Ramanujam , P. Sadayappan

One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the…

Computational Complexity · Computer Science 2021-03-09 Troy Lee , Adi Shraibman

In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…

Logic · Mathematics 2020-08-21 Raheleh Jalali

We consider succinct data structures for representing a set of $n$ horizontal line segments in the plane given in rank space to support \emph{segment access}, \emph{segment selection}, and \emph{segment rank} queries. A segment access query…

Data Structures and Algorithms · Computer Science 2024-12-09 Philip Bille , Inge Li Gørtz , Simon R. Tarnow

We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…

Programming Languages · Computer Science 2024-12-06 Fabian Zaiser , Andrzej S. Murawski , C. -H. Luke Ong

We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our…

Data Structures and Algorithms · Computer Science 2007-10-18 David Talbot , John Talbot