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Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.


Papers
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01 May 2002
TL;DR: This work speculates on computational aspects of certain discontinuous functions by taking the Gau ian function [x] as a typical example and studying it in the light of the notions of upper semi-computability and of limiting computation.
Abstract: We speculate on computational aspects of certain discontinuous functions by taking the Gau ian function [x] as a typical example. An algorithm how to compute [x] for a single computable real number is rst described, followed by a remark that [x] does not necessarily preserve sequential computability. Second, [x] is studied in the light of the notions of upper semi-computability and of limiting computation. Then two Fr echet spaces, Rand L1loc(R) , in which some discontinuous functions will become computable, will be taken up.

17 citations

Book
07 Jun 2013
TL;DR: In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of the authors' modern understanding.
Abstract: In the 1930s a series of seminal works published by Alan Turing, Kurt Gdel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gdel, and Church, including the Church-Turing thesis and Gdel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gdel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors:Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

17 citations

Journal ArticleDOI
01 Dec 1960-Synthese
TL;DR: There are nowadays two kinds of computers: digital computers and analogue computers; the principal distinction is this.
Abstract: There are nowadays two kinds of computers: digital computers and analogue computers. The principal distinction is this. The questions and answers of a digital computer are presented in symbolic form, perhaps printed on a tape or on cards. An analogue computer, on the other hand, relies on the dependence of one physical magnitude on another. For example, the question (or the input) may be an electrical voltage, and the answer (or output) another voltage related to the first in a manner determined by the structure of the machine.

17 citations

Journal Article
TL;DR: A number of classes of X-machines are investigated and it is shown that a certain class of these machines the 2-stack straight move stream X-machine computes precisely the class of partial recursive functions.
Abstract: The theory of computable functions is well known and has given rise to many classes of computational models of varying power and usefullness. We take another look at this subject using the idea of a generalised machine the X-machine to provide some further insights into the issue and to discuss an elegant general approach to the question of classifying computational models including some of the socalled "Super-Turing" models. This paper investigates a number of classes of X-machines. It considers their relative computational capabilities and contrasts these with other important models. It is shown that a certain class of these machines the 2-stack straight move stream X-machine computes precisely the class of partial recursive functions. The importance of this work to the theory of testing of systems is

17 citations

Book ChapterDOI
07 Oct 2019
TL;DR: This work refine the classic notions of monitorability, both for trace properties and hyperproperties, taking into account the computability of the monitor, to monitor a privacy hyperproperty called distributed data minimality, expressed as a HyperLTL property, by using an SMT-based static verifier at runtime.
Abstract: Many important system properties, particularly in security and privacy, cannot be verified statically. Therefore, runtime verification is an appealing alternative. Logics for hyperproperties, such as HyperLTL, support a rich set of such properties. We first show that black-box monitoring of HyperLTL is in general unfeasible, and suggest a gray-box approach. Gray-box monitoring implies performing analysis of the system at run-time, which brings new limitations to monitorability (the feasibility of solving the monitoring problem). Thus, as another contribution of this paper, we refine the classic notions of monitorability, both for trace properties and hyperproperties, taking into account the computability of the monitor. We then apply our approach to monitor a privacy hyperproperty called distributed data minimality, expressed as a HyperLTL property, by using an SMT-based static verifier at runtime.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202344
2022119
202189
202098
2019111
201897