In 1990 Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem (CCV). He and Mayr showed that NL \subseteq CC \subseteq P, and proved that in addition to CCV several other proble...
RoboCup offers a set of benchmark problems for Artificial Intelligence in form of official world championships since 1997. The most tactical advanced and richest in terms of behavioural complexity of these is the 2D Soccer Simulation League, a simula...
Based on [1], we study the complexity of horizontality in each twistor space $\hat{E}_{\varepsilon}$ associated with an oriented vector bundle $E$ of rank $4$ with a positive-definite metric over the $2$-torus $T^2$, and obtain classification of the...
In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological complexity, with each other in digital images. For some certain digital images, we introduce $κ-$...
Digital topological methods are often used on computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a digitally...
The rapid expansion of global cloud infrastructures, coupled with the growing volume and complexity of network traffic, has fueled active research into scalable and resilient Traffic Engineering (TE) solutions for Wide Area Networks (WANs). Despite r...
Understanding the computational complexity of learning efficient classical programs in various learning models has been a fundamental and important question in classical computational learning theory. In this work, we study the computational complexi...
We study the menu complexity of optimal and approximately-optimal auctions in the context of the "FedEx" problem, a so-called "one-and-a-half-dimensional" setting where a single bidder has both a value and a deadline for receiving an [FGKK16]. The me...
$T$-varieties are normal varieties equipped with an action of an algebraic torus $T$. When the action is effective, the complexity of a $T$-variety $X$ is $\dim(X)-\dim(T)$. Matrix Schubert varieties, introduced by Fulton in 1992, are $T$-varieties c...
We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of such algo...
After Strassen presented the first sub-cubic matrix multiplication algorithm, many Strassen-like algorithms are presented. Most of them with low asymptotic cost have large hidden leading coefficient which are thus impractical. To reduce the leading c...
Let $G=\left\langle S|R_{A}\right\rangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological entropies. After...
We study the average case complexity of the uniform membership problem for subgroups of free groups, and we show that it is orders of magnitude smaller than the worst case complexity of the best known algorithms. This applies to subgroups given by a...
Max Independent Set (MIS) is a paradigmatic problem in theoretical computer science and numerous studies tackle its resolution by exact algorithms with non-trivial worst-case complexity. The best such complexity is, to our knowledge, the $O^*(1.188...
The complexity of multimedia applications in terms of intensity of computation and heterogeneity of treated data led the designers to embark them on multiprocessor systems on chip. The complexity of these systems on one hand and the expectations of...
We revisit the periodic complexity function $h_{\bf w}(n)$ introduced by Mignosi and Restivo. This function gives the average of the first $n$ local periods of a recurrent infinite word ${\bf w}$. We give a different method than that of Mignosi and R...
We investigate the complexity of several manipulation and control problems under numerous prevalent approval-based multiwinner voting rules. Particularly, the rules we study include approval voting (AV), satisfaction approval voting (SAV), net-satisf...
It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the variable ord...
particularly computational complexity theory. At Cornell, he became interested in quantum computing and devoted himself to computational complexity and quantum
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of various versi...
Previous work of the second author and Wolf showed that given a set $A\subseteq \mathbb{F}_p^n$ of bounded $\textrm{VC}_2$-dimension, there is a high rank quadratic factor $\mathcal{B}$ of bounded complexity such that $A$ is approximately equal to a...
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance....
We introduce an idea called anti-gadgets in complexity reductions. These combinatorial gadgets have the effect of erasing the presence of some other graph fragment, as if we had managed to include a negative copy of a graph gadget. We use this idea t...
We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index $i$ such that $x_i\neq y_i$, i...
We present a comparative analysis of text complexity across domains using scale-free metrics. We quantify linguistic complexity via Heaps' exponent $β$ (vocabulary growth), Taylor's exponent $α$ (word-frequency fluctuation scaling), compression rat...
These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne on Septemb...
The complexity of mathematical models describing respiratory mechanics has grown in recent years to integrate with cardiovascular models and incorporate nonlinear dynamics. However, additional model complexity has rarely been studied in the context o...
The letter by Mark Perakh entitled "DEFINING COMPLEXITY: A Commentary to a paper by Charles H. Bennett" is here archived with the permission of the author. This letter was downloaded from the site "On Talk Reason, http://www.talkreason.org/articles...
Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity patterns to...
We study the complexity of learning mixtures of separated Gaussians with common unknown bounded covariance matrix. Specifically, we focus on learning Gaussian mixture models (GMMs) on $\mathbb{R}^d$ of the form $P= \sum_{i=1}^k w_i \mathcal{N}(\bolds...
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this task that have been applicable to a wide range of contexts. In particu...
We consider conjunctive queries with arithmetic comparisons (CQAC) and investigate the computational complexity of the problem: Given two CQAC queries, $Q$ and $Q'$, is $Q'$ contained in $Q$? We know that, for CQAC queries, the problem of testing con...
Recently, there has been remarkable progress in reinforcement learning (RL) with general function approximation. However, all these works only provide regret or sample complexity guarantees. It is still an open question if one can achieve stronger pe...
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more interpretable, sever...
We provide new insights on eluder dimension, a complexity measure that has been extensively used to bound the regret of algorithms for online bandits and reinforcement learning with function approximation. First, we study the relationship between the...
"green dragon book" and its cover depicts a knight and a dragon in battle; the dragon is green, and labeled "Complexity of Compiler Design", while the knight
Jan 20, 2026 · Adjective intricate (comparative more intricate, superlative most intricate) Having a great deal of fine detail or complexity. Synonyms: fancy, convoluted The architecture of this clock is very …
Jan 20, 2026 · Adjective intricate (comparative more intricate, superlative most intricate) Having a great deal of fine detail or complexity. Synonyms: fancy, convoluted The architecture of this clock is very …
Modern model-free reinforcement learning methods have recently demonstrated impressive results on a number of problems. However, complex domains like dexterous manipulation remain a challenge due to the high sample complexity. To address this, curren...
Jan 23, 2026 · Trade was a major topic of discussion at the Annual Meeting 2026 in Davos. Expert participants examined everything from how geopolitical complexity is accelerating trade deals to the …