Related papers: A Hierarchy for Constant Communication Complexity
We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples of such models include Boolean circuits, membrane systems, DNA computers, chemical…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
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…
Classifications organize entities into categories that identify similarities within a category and discern dissimilarities among categories, and they powerfully classify information in support of analysis. We propose a new classification…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an…
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure $\mathcal{R}$, and we show that under weak conditions on $\mathcal{R}$, the complexity class $\text{NP}(\mathcal{R})$…
In Ordinal Classification tasks, items have to be assigned to classes that have a relative ordering, such as positive, neutral, negative in sentiment analysis. Remarkably, the most popular evaluation metrics for ordinal classification tasks…
To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
The $\pi$-calculus is a process algebra where agents interact by sending communication links to each other via noiseless communication channels. Taking into account the reality of noisy channels, an extension of the $\pi$-calculus, called…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
We study the communication complexity of computing functions $F:\{0,1\}^n\times \{0,1\}^n \rightarrow \{0,1\}$ in the memoryless communication model. Here, Alice is given $x\in \{0,1\}^n$, Bob is given $y\in \{0,1\}^n$ and their goal is to…
This work addresses two problems in the context of two-party communication complexity of functions. First, it concludes the line of research, which can be viewed as demonstrating qualitative advantage of quantum communication in the three…
We study the complexity of reasoning in abstracts argumentation frameworks close to graph classes that allow for efficient reasoning methods, i.e.\ to one of the classes of acyclic, noeven, biparite and symmetric AFs. In this work we show…
We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem…
To study the communication between information systems, Wang et al. [C. Wang, C. Wu, D. Chen, Q. Hu, and C. Wu, Communicating between information systems, Information Sciences 178 (2008) 3228-3239] proposed two concepts of type-1 and type-2…