相关论文: In Memory of Martin Davis

This work exposes which mechanisms and procesess in the Nature of evolution compute a function not computable by Turing machine. The computer with intelligence that is not higher than one bacteria population could have, but with efficency…

In this paper we present an introduction to the area of computability in dynamical systems. This is a fairly new field which has received quite some attention in recent years. One of the central questions in this area is if relevant…

This note is about encoding Turing machines into the lambda-calculus.

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…

The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here…

We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…

The term `hypermachine' denotes any data processing device (theoretical or that can be implemented) capable of carrying out tasks that cannot be performed by a Turing machine. We present a possible quantum algorithm for a classically…

We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.

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.

A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.

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 introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…

The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…

These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…

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…

We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem…

There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture on Turing invariant functions. This longstanding open problem…

Since the Turing test was first proposed by Alan Turing in 1950, the primary goal of artificial intelligence has been predicated on the ability for computers to imitate human behavior. However, the majority of uses for the computer can be…

The world has seen the emergence of machines based on pretrained models, transformers, also known as generative artificial intelligences for their ability to produce various types of content, including text, images, audio, and synthetic…

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…