相关论文: Hypercomputation: computing more than the Turing m…
We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones.…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
Quantum computing has the potential to provide exponential performance benefits in processing over classical computing. It utilizes quantum mechanics phenomena (such as superposition, entanglement, and interference) to solve a computational…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
The machinery of the human brain -- analog, probabilistic, embodied -- can be characterized computationally, but what machinery confers what computational powers? Any such system can be abstractly cast in terms of two computational…
We show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective…
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…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
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.…
The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the…
Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging…