Related papers: Axiomatic Tools versus Constructive approach to Un…

In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the…

Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer…

I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…

In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…

This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…

Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…

Recent research increasingly brings to question the appropriateness of using predictive tools in complex, real-world tasks. While a growing body of work has explored ways to improve value alignment in these tools, comparatively less work…

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…

We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…

People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…

The introduction of new tools in people's workflow has always been promotive of new creative paths. This paper discusses the impact of using computational tools in the performance of creative tasks, especially focusing on graphic design.…

As the world's democratic institutions are challenged by dissatisfied citizens, political scientists and also computer scientists have proposed and analyzed various (innovative) methods to select representative bodies, a crucial task in…

Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization,…

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

I think that the main reason why we do not understand the general principles of how knowledge works (and probably also the reason why we have not yet designed and built efficient machines capable of artificial intelligence), is not the…

From self-driving vehicles and back-flipping robots to virtual assistants who book our next appointment at the hair salon or at that restaurant for dinner - machine learning systems are becoming increasingly ubiquitous. The main reason for…

Algorithmic solutions have significant potential to improve decision-making across various domains, from healthcare to e-commerce. However, the widespread adoption of these solutions is hindered by a critical challenge: the lack of…

Most work on computational complexity is concerned with time. However this course will try to show that program-size complexity, which measures algorithmic information, is of much greater philosophical significance. I'll discuss how one can…