Related papers: The Machine as Data: A Computational View of Emerg…
The field of computability and complexity was, where computer science sprung from. Turing, Church, and Kleene all developed formalisms that demonstrated what they held "intuitively computable". The times change however and today's…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
Society's capacity for algorithmic problem-solving has never been greater. Artificial Intelligence is now applied across more domains than ever, a consequence of powerful abstractions, abundant data, and accessible software. As capabilities…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventually to a nuanced conclusion.
The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…
This article is an attempt to generalize the classical theory of reversible computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum case.…
In this chapter, we argue for an epistemological shift from viewing coding and computational thinking as mastery over computational logic and symbolic forms, to viewing them as a more complex form of experience. Rather than viewing…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
This paper proposes a specific conceptualization of intelligence as computation. This conceptualization is intended to provide a unified view for all disciplines of intelligence research. Already, it unifies several conceptualizations…
With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Machine learning is a computational process. To that end, it is inextricably tied to computational power - the tangible material of chips and semiconductors that the algorithms of machine intelligence operate on. Most obviously,…
Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
We propose an explanatory and computational theory of transformative discoveries in science. The theory is derived from a recurring theme found in a diverse range of scientific change, scientific discovery, and knowledge diffusion theories…