Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required to be loc...
In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash equilibria in...
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction problems, we deve...
We prove that computing the deterministic communication complexity D(f) of a Boolean function is NP-hard in the standard protocol-tree model, answering, independently and concurrently with Hirahara-Llango-Loff (arXiv:2507.10426), a question first pos...
Cities are complex systems, their complexity manifests itself through fractality of their spatial structures and by power law distributions (scaling) of multiple urban attributes. Here we report on the previously unreported manifestation of urban com...
Free/Open Source Software (FOSS) enables large-scale reuse of preexisting software components. The main drawback is increased complexity in software supply chain management. A common approach to tame such complexity is automated open source complianc...
We study the complexity of computing Kronecker coefficients $g(λ,μ,ν)$. We give explicit bounds in terms of the number of parts $\ell$ in the partitions, their largest part size $N$ and the smallest second part $M$ of the three partitions. When $M...
We define a new model of communication complexity, called the garden-hose model. Informally, the garden-hose complexity of a function f:{0,1}^n x {0,1}^n to {0,1} is given by the minimal number of water pipes that need to be shared between two partie...
We study the sample complexity of teaching, termed as "teaching dimension" (TDim) in the literature, for the teaching-by-reinforcement paradigm, where the teacher guides the student through rewards. This is distinct from the teaching-by-demonstration...
The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating the process of preparation, transmission through the channel, and subsequent measurement of a quantum state. At pre...
This study investigates whether diagnostic prompting can improve Multimodal Large Language Model (MLLM) reliability for visual complexity assessment of Amazon Search Results Pages (SRP). We compare diagnostic prompting with standard gestalt principle...
We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length...
Entanglement is the defining characteristic of quantum mechanics. Bipartite entanglement is characterized by the von Neumann entropy. Entanglement is not just described by a number, however; it is also characterized by its level of complexity. The co...
Automotive traffic is a classical example of a complex system, being the simplest case the homogeneous traffic where all vehicles are of the same kind, and using different means of transportation increases complexity due to different driving rules an...
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were sugg...
For a finite word $w$ we define and study the Kolmogorov structure function $h_w$ for nondeterministic automatic complexity. We prove upper bounds on $h_w$ that appear to be quite sharp, based on numerical evidence....
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 $κ-$...