Related papers: Some Thoughts on Hypercomputation
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and…
The design of any technical Computer Science course must involve its context within the institution's CS program, but also incorporate any new material that is relevant and appropriately accessible to students. In many institutions, theory…
An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the…
Alan Turing is considered as a founder of current computer science together with Kurt Godel, Alonzo Church and John von Neumann. In this paper multiple new research results are presented. It is demonstrated that there would not be Alan…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and…
The "easy" problem of cognitive science is explaining how and why we can do what we can do. The "hard" problem is explaining how and why we feel. Turing's methodology for cognitive science (the Turing Test) is based on doing: Design a model…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
Recent investigations into the physical nature of information and fundamental limits to information transmission have revealed questions such as the possibility of superluminal data transfer or not; and whether reversible computation…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
Computing is an indispensable component of nearly all technologies and is ubiquitous for vast segments of society. It is also essential to discoveries and innovations in most disciplines. However, while past grand challenges in science have…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…
This book develops the conjecture that all kinds of information processing in computers and in brains may usefully be understood as "information compression by multiple alignment, unification and search". This "SP theory", which has been…
This piece plays with the idea of the Computocene: an era defined not merely by the ubiquity of computers, but by their deepening role in how we observe, interpret, and make sense of the world. Rather than emphasizing automation, speed,…
Possible for science itself, conceptually, to have and will understand differently, let alone science also seen as technology, such as computer science. After all, science and technology are viewpoints diverse by either individual,…