The Universal Machine

2017 ◽  
Author(s):  
Arlindo Oliveira
Keyword(s):  
Computer Science ◽  
Turing Machine ◽  
Universal Machine ◽  
Alan Turing ◽  
Modern Computer ◽  
Basic Concepts ◽  
The Church

This chapter covers the development of computing, from its origins, with the analytical engine, to modern computer science. Babbage and Ada Lovelace’s contributions to the science of computing led, in time, to the idea of universal computers, proposed by Alan Turing. These universal computers, proposed by Turing, are conceptual devices that can compute anything that can possibly be computed. The basic concepts created by Turing and Church were further developed to create the edifice of modern computer science and, in particular, the concepts of algorithms, computability, and complexity, covered in this chapter. The chapter ends describing the Church-Turing thesis, which states that anything that can be computed can be computed by a Turing machine.

Decidability and the Entscheidungsproblem

2017 ◽  
Author(s):  
Robin Whitty
Keyword(s):  
Mathematical Model ◽  
Computer Science ◽  
20Th Century ◽  
Turing Machine ◽  
Human Computation ◽  
Early 20Th Century ◽  
Binary Representation ◽  
The Third ◽  
Alan Turing ◽  
Modern Computer

In 1936 Turing invented a mathematical model of computation, known today as the Turing machine. He intended it as a representation of human computation and in particular as a vehicle for refuting a central part of David Hilbert’s early 20th-century programme to mechanize mathematics. By a nice irony it came to define what is achievable by non-human computers and has become deeply embedded in modern computer science. A simple example is enough to convey the essentials of a Turing machine. We then describe the background to Hilbert’s programme and Turing’s challenge—and explain how Turing’s response to Hilbert resolves a host of related problems in mathematics and logic. If I had to portray, in less than 30 seconds, what Alan Turing achieved in 1936 it seems to me that drawing the picture shown in Fig. 37.1 would be a reasonable thing to do. That this might be so is a testament to the quite extraordinary merging of the concrete and the abstract in Turing’s 1936 paper on computability. It is regarded by, I suppose, a large majority of mathematical scientists as his greatest work. The details of our picture are not especially important. As it happens, it is a machine for deciding which whole numbers, written in binary form, are multiples of 3. It works thus: suppose the number is 105, whose binary representation is 1101001, because (1 × 26) + (1 × 25) + (0 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20) = 64 + 32 + 8 + 1 = 105. We start at the node labelled A and use the binary digits to drive us from node to node. The first couple of 1s take us to node B and back to A again. The third digit, 0, loops us around at A. Now a 1 and a 0 take us across to node C; and the final 0 and 1 take us back via B to A once more.

scholarly journals ФУНДАМЕНТАЛЬНІ ПОНЯТТЯ ЯК ІНТЕГРАТИВНИЙ КОМПОНЕНТ ОРГАНІЗАЦІЇ НАВЧАННЯ ДОСЛІДЖЕННЯ ОПЕРАЦІЙ МАЙБУТНІХ БАКАЛАВРІВ ІНФОРМАТИКИ

2016 ◽  
Vol 52 (2) ◽  
pp. 36
Author(s):  
Ulyana P. Kogut
Keyword(s):  
Computer Science ◽  
Operations Research ◽  
Educational Process ◽  
Integrated System ◽  
Modern Computer ◽  
Basic Concepts ◽  
Theoretical Foundations ◽  
Knowledge In Practice

The article analyzes the role of basic concepts of operations research in teaching of future bachelor of computer science. On the basis of the analysis it was determined the possible use of modern computer mathematics systems (CMS) as a means of educational process fundamentalization. Singling out the basic concepts of operations research, their understanding through experience of research is integrable component of training, the establishment of inter-subject relationship, the formation of an integrated system of students’ knowledge and understanding of both the theoretical foundations and the ways to use the acquired knowledge in practice. Also the role of CMS in training bachelors of computer science, the directions of the pedagogical use of CMS in studying of operations research are considered.

2. Computational artefacts

2016 ◽  
pp. 13-32
Author(s):  
Subrata Dasgupta
Keyword(s):  
Computer Science ◽  
Turing Machine ◽  
Abstraction Refinement ◽  
Modern Computer ◽  
Means And Ends ◽  
Rules And Principles ◽  
Human Need ◽  
Compositional Hierarchy ◽  
The Relationship

The modern computer is a hierarchically organized system of computational artefacts. Inventing, understanding, and applying rules and principles of hierarchy is a subdiscipline of computer science. ‘Computational artefacts’ explains the concepts of compositional hierarchy, the abstraction/refinement principle, and hierarchy by construction. There are three classes of computational artefacts—abstract, material, and liminal. An important example of an abstract artefact is the Turing machine. Sciences involving artefacts are sciences of the artificial, entailing the study of the relationship between means and ends. The ‘science’ in computer science is, thus, a science of means and ends. It asks: how can a computational artefact demonstrably achieve a given human need, goal, or purpose?

scholarly journals From Computer Science to the Informational Worldview. Philosophical Interpretations of Some Computer Science Concepts

2019 ◽  
Vol 44 (1) ◽  
pp. 27-43 ◽  
Author(s):  
Paweł Stacewicz
Keyword(s):  
Information Processing ◽  
Data Processing ◽  
Computer Science ◽  
Turing Machine ◽  
Processing System ◽  
Informational Content ◽  
Basic Assumptions ◽  
Modern Computer ◽  
Science Concepts ◽  
The Mind

AbstractIn this article I defend the thesis that modern computer science has a significant philosophical potential, which is expressed in a form of worldview, called here informational worldview (IVW). It includes such theses like: a) each being contains a certain informational content (which may be revealed by computer science concepts, such as code or algorithm), b) the mind is an information processing system (which should be modeled by means of data processing systems), c) cognition is a type of computation. These (pre)philosophical theses are accepted in many sciences (e.g. in cognitive science), and this is both an expression and strengthening of the IWV. After a general discussion of the relations between philosophy, particular sciences and the worldview, and then the presentation of the basic assumptions and theses of the IWV, I analyze a certain specification of thesis b) expressed in the statement that “the mind is the Turing machine”. I distinguish three concepts of mind (static, variable and minimal) and explain how each of them is connected with the concept of the Turing machine.

IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?

2002 ◽  
Vol 85 (2) ◽  
pp. 312-332 ◽  
Author(s):  
KLAUS WEIHRAUCH ◽  
NING ZHONG
Keyword(s):  
Wave Propagation ◽  
Turing Machine ◽  
Sobolev Spaces ◽  
Three Dimensional ◽  
Subject Classification ◽  
Physical Machine ◽  
The Church ◽  
Dimensional Wave

According to the Church-Turing Thesis a number function is computable by the mathematically defined Turing machine if and only if it is computable by a physical machine. In 1983 Pour-El and Richards defined a three-dimensional wave $u(t,x)$ such that the amplitude $u(0,x)$ at time 0 is computable and the amplitude $u(1,x)$ at time 1 is continuous but not computable. Therefore, there might be some kind of wave computer beating the Turing machine. By applying the framework of Type 2 Theory of Effectivity (TTE), in this paper we analyze computability of wave propagation. In particular, we prove that the wave propagator is computable on continuously differentiable waves, where one derivative is lost, and on waves from Sobolev spaces. Finally, we explain why the Pour-El-Richards result probably does not help to design a wave computer which beats the Turing machine.2000 Mathematical Subject Classification: 03D80, 03F60, 35L05, 68Q05.

Computer science

2021 ◽  
Author(s):  
Vladimir Yashin ◽  
Anna Kolodenkova
Keyword(s):  
Computer Science ◽  
Information Technologies ◽  
Computer Software ◽  
Theoretical Computer Science ◽  
Educational Institutions ◽  
Federal State ◽  
University Teachers ◽  
Modern Computer ◽  
Information Models ◽  
State Educational

The book describes the main topics of modern computer science: branch of theoretical computer science, associated with the analysis of different information models; section of computer technology, dedicated to the development of common principles of computer systems; section of programming devoted to the principles of algorithms and computer software. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying information technologies in the framework of the discipline "Informatics", graduate students, university teachers and anyone interested in modern information technologies.

ENIAC and Its Contemporaries Meet the “Stored Program Concept”

2016 ◽  
Author(s):  
Thomas Haigh ◽  
Mark Priestley ◽  
Crispin Rope
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Modern Computer ◽  
Initial Implementation ◽  
Previous Discussion ◽  
Actual Use ◽  
Desk Calculator ◽  
The Senses ◽  
Over Time

Having explored ENIAC’s actual use and the programs it ran the authors shift to a more abstract analytical level. Previous discussion of the invention of the modern computer has focused on the “stored program concept” as the crucial innovation setting modern computers apart from their more limited predecessors. The authors explore the origins of this phrase and its changing meaning over time. They look in detail at a 1944 document produced by J. Presper Eckert and sometimes claimed as a first statement of this concept, showing that it actually describes an electronic desk calculator. The authors summarize ENIAC’s capabilities after conversion and to compare these on both practical and theoretical levels with the 1945 EDVAC design and with several other early computers. This supports a balanced appraisal of the senses in which the converted ENIAC did and did not constitute an initial implementation of the key ideas from the 1945 design. The chapter argues for an appraisal of early computers better grounded in the historical realities of documented use, and against a widespread fixation on the notion of “universality” based on a school of theoretical computer science that gained prominence years later.

A Liminal Artifact of an Uncommon Nature

2014 ◽  
Author(s):  
Subrata Dasgupta
Keyword(s):  
Turing Machine ◽  
Major Part ◽  
Physical Reality ◽  
Physical World ◽  
The Other ◽  
Symbol Manipulation ◽  
Physical Machine ◽  
Essential Nature ◽  
Alan Turing ◽  
The One

The story so far has been a narrative about the development of two very contrasting types of computational artifacts. On the one hand, Alan Turing conceived the idea of a purely abstract and formal artifact—the Turing machine—having no physical reality whatsoever, an artifact that belongs to the same realm of symbols and symbol manipulation, as do mathematical objects. On the other hand, the major part of this narrative has been concerned with a material artifact, the computer as a physical machine that, ultimately, must obey the laws of physics—in particular, the laws governing electromagnetism and mechanics. This was as true for Babbage’s machines (which were purely mechanical) as for Hollerith’s tabulator, as true for the electromechanical machines, as for the Harvard Mark I and the Bell Telephone computers, as true for the ABC and the ENIAC, as for the EDSAC and the Manchester Mark I. Beginning with the EDVAC report, and especially manifest in the development of the first operational stored-program computers, was the dawning awareness of a totally new kind of artifact, the likes of which had never been encountered before. Philosophers speak of the ontology of something to mean the essential nature of that thing, what it means to be that thing. The ontology of this new kind of artifact belonged neither to the familiar realm of the physical world nor the equally familiar realm of the abstract world. Rather, it had characteristics that looked toward both the physical and the abstract. Like Janus, the Roman god of gates, it looked in two opposite directions: a two-faced artifact—which, as we will see, served as the interface between the physical and the abstract, between the human and the automaton; a liminal artifact, hovering ontologically between and betwixt the material and the abstract (see Prologue, Section IV ). So uncommon was this breed that even a name for it was slow to be coined. During the Cambridge conference in England in 1949, we find a session devoted to programming and coding.

New £50 Celebrates Turing’s Achievements

ITNOW ◽  
2019 ◽  
Vol 61 (4) ◽  
pp. 32-33
Author(s):  
Johanna Hamilton
Keyword(s):  
Computer Science ◽  
Alan Turing ◽  
Bank Of England

Abstract Johanna Hamilton interviews Sarah John, Chief Cashier of the Bank of England, about the decision to feature Alan Turing, the father of computer science, on the new £50 note.

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