Related papers: Report on Generic Case Complexity
What is a complex network? How do we characterize complex networks? Which systems can be studied from a network approach? In this text, we motivate the use of complex networks to study and understand a broad panoply of systems, ranging from…
Explainable AI has garnered considerable attention in recent years, as understanding the reasons behind decisions or predictions made by AI systems is crucial for their successful adoption. Explaining classifiers' behavior is one prominent…
The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
A generic computation of a subset A of the natural numbers consists of a a computation that correctly computes most of the bits of A, and which never incorrectly computes any bits of A, but which does not necessarily give an answer for…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to…
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…