Related papers: Editors' remarks (on two complexity theory surveys…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
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…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results…
The paper serves as the first contribution towards the development of the theory of efficiency: a unifying framework for the currently disjoint theories of information, complexity, communication and computation. Realizing the defining…
A discussion of fundamental aspects of quantum theory is presented, stressing the essential role of "events". (Abstract by Erhard Seiler -- see afterword)
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to…
This is an expository paper about the Borel complexity of structure and classification theorems. It sorts several classical problems relative to known benchmarks of complexity. As a corollary various problems proposed by people such as von…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
In this position paper we discuss three main shortcomings of existing approaches to counterfactual causality from the computer science perspective, and sketch lines of work to try and overcome these issues: (1) causality definitions should…
Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
News articles of varying degrees of truthfulness and political alignment, and their influences on the political opinions of the media consumers are modeled as a Bayesian network incorporating a mixture of ideas from dual-reasoning models of…
This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the…
In this article a revised, to some extent, version of the Information concept as utmost fundamental essence ("The Information and the Matter",v1) is presented - a little more logical grounds and may be of a philosophy, the correction and…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.
We comment on a recent paper by D'Abramo [Chaos, Solitons & Fractals, 25 (2005) 29], focusing on the author's statement that an algorithm can produce a list of strings containing at least one string whose algorithmic complexity is greater…