Related papers: Incomputability after Alan Turing
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
Contemporary concerns over the governance of technological systems often run up against narratives about the technical infeasibility of designing mechanisms for accountability. While in recent AI ethics literature these concerns have 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,…
Computational complexity has often been ignored in philosophy of mind, in philosophical artificial intelligence studies. The purpose of this paper is threefold. First and foremost, to show the importance of complexity rather than…
Charles Babbage's vision of computing has largely been realized. We are on the verge of realizing Vannevar Bush's Memex. But, we are some distance from passing the Turing Test. These three visions and their associated problems have provided…
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…
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…
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…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…