Related papers: A Statistical Measure of Complexity
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.
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…
Software code complexity is a well-studied property to determine software component health. However, the existing code complexity metrics do not directly take into account the fault-proneness aspect of the code. We propose a metric called…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
Software implements a significant proportion of functionality in factory automation. Thus, efficient development and the reuse of software parts, so-called units, enhance competitiveness. Thereby, complex control software units are more…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
In this paper, we introduce the new concept of state complexity approximation, which is a further development of state complexity estimation. We show that this new concept is useful in both of the following two cases: the exact state…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Software systems are expansive, exhibiting behaviors characteristic of complex systems, such as self-organization and emergence. These systems, highlighted by advancements in Large Language Models (LLMs) and other AI applications developed…
In this note, we discuss a number of parametricity features and what their requirements are in terms of complexity of the type system and its model.
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
This paper presents a series of general properties of the r-Complexity calculus, a complexity measurement for assessing the performance and asymptotic behaviour of real-world algorithms. This research describes characteristics such as…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in the topological diversity of the assigned graphs, resulting from a resolution of their…
Nanostructured surfaces usually exhibit complicated morphologies that cannot be described in terms of Euclidean geometry. Simultaneously, they do not constitute fully random noise fields to be characterized by simple stochastics and…