Alan Turing: Thinking the Unthinkable, Solving the Unsolvable
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Elementary Functions: Towards Automatically Generated, Efficient
Elementary functions : towards automatically generated, efficient, and vectorizable implementations Hugues De Lassus Saint-Genies To cite this version: Hugues De Lassus Saint-Genies. Elementary functions : towards automatically generated, efficient, and vectorizable implementations. Other [cs.OH]. Université de Perpignan, 2018. English. NNT : 2018PERP0010. tel-01841424 HAL Id: tel-01841424 https://tel.archives-ouvertes.fr/tel-01841424 Submitted on 17 Jul 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Délivré par l’Université de Perpignan Via Domitia Préparée au sein de l’école doctorale 305 – Énergie et Environnement Et de l’unité de recherche DALI – LIRMM – CNRS UMR 5506 Spécialité: Informatique Présentée par Hugues de Lassus Saint-Geniès [email protected] Elementary functions: towards automatically generated, efficient, and vectorizable implementations Version soumise aux rapporteurs. Jury composé de : M. Florent de Dinechin Pr. INSA Lyon Rapporteur Mme Fabienne Jézéquel MC, HDR UParis 2 Rapporteur M. Marc Daumas Pr. UPVD Examinateur M. Lionel Lacassagne Pr. UParis 6 Examinateur M. Daniel Menard Pr. INSA Rennes Examinateur M. Éric Petit Ph.D. Intel Examinateur M. David Defour MC, HDR UPVD Directeur M. Guillaume Revy MC UPVD Codirecteur À la mémoire de ma grand-mère Françoise Lapergue et de Jos Perrot, marin-pêcheur bigouden. -
Reconfigurable Embedded Control Systems: Problems and Solutions
RECONFIGURABLE EMBEDDED CONTROL SYSTEMS: PROBLEMS AND SOLUTIONS By Dr.rer.nat.Habil. Mohamed Khalgui ⃝c Copyright by Dr.rer.nat.Habil. Mohamed Khalgui, 2012 v Martin Luther University, Germany Research Manuscript for Habilitation Diploma in Computer Science 1. Reviewer: Prof.Dr. Hans-Michael Hanisch, Martin Luther University, Germany, 2. Reviewer: Prof.Dr. Georg Frey, Saarland University, Germany, 3. Reviewer: Prof.Dr. Wolf Zimmermann, Martin Luther University, Germany, Day of the defense: Monday January 23rd 2012, Table of Contents Table of Contents vi English Abstract x German Abstract xi English Keywords xii German Keywords xiii Acknowledgements xiv Dedicate xv 1 General Introduction 1 2 Embedded Architectures: Overview on Hardware and Operating Systems 3 2.1 Embedded Hardware Components . 3 2.1.1 Microcontrollers . 3 2.1.2 Digital Signal Processors (DSP): . 4 2.1.3 System on Chip (SoC): . 5 2.1.4 Programmable Logic Controllers (PLC): . 6 2.2 Real-Time Embedded Operating Systems (RTOS) . 8 2.2.1 QNX . 9 2.2.2 RTLinux . 9 2.2.3 VxWorks . 9 2.2.4 Windows CE . 10 2.3 Known Embedded Software Solutions . 11 2.3.1 Simple Control Loop . 12 2.3.2 Interrupt Controlled System . 12 2.3.3 Cooperative Multitasking . 12 2.3.4 Preemptive Multitasking or Multi-Threading . 12 2.3.5 Microkernels . 13 2.3.6 Monolithic Kernels . 13 2.3.7 Additional Software Components: . 13 2.4 Conclusion . 14 3 Embedded Systems: Overview on Software Components 15 3.1 Basic Concepts of Components . 15 3.2 Architecture Description Languages . 17 3.2.1 Acme Language . -
YANLI: a Powerful Natural Language Front-End Tool
AI Magazine Volume 8 Number 1 (1987) (© AAAI) John C. Glasgow I1 YANLI: A Powerful Natural Language Front-End Tool An important issue in achieving acceptance of computer sys- Since first proposed by Woods (1970), ATNs have be- tems used by the nonprogramming community is the ability come a popular method of defining grammars for natural to communicate with these systems in natural language. Of- language parsing programs. This popularity is due to the ten, a great deal of time in the design of any such system is flexibility with which ATNs can be applied to hierarchically devoted to the natural language front end. An obvious way to describable phenomenon and to their power, which is that of simplify this task is to provide a portable natural language a universal Turing machine. As discussed later, a grammar front-end tool or facility that is sophisticated enough to allow in the form of an ATN (written in LISP) is more informative for a reasonable variety of input; allows modification; and, than a grammar in Backus-Naur notation. As an example, yet, is easy to use. This paper describes such a tool that is the first few lines of a grammar for an English sentence writ- based on augmented transition networks (ATNs). It allows ten in Backus-Naur notation might look like the following: for user input to be in sentence or nonsentence form or both, provides a detailed parse tree that the user can access, and sentence : := [subject] predicate also provides the facility to generate responses and save in- subject ::= noun-group formation. -
The Advent of Recursion & Logic in Computer Science
The Advent of Recursion & Logic in Computer Science MSc Thesis (Afstudeerscriptie) written by Karel Van Oudheusden –alias Edgar G. Daylight (born October 21st, 1977 in Antwerpen, Belgium) under the supervision of Dr Gerard Alberts, and submitted to the Board of Examiners in partial fulfillment of the requirements for the degree of MSc in Logic at the Universiteit van Amsterdam. Date of the public defense: Members of the Thesis Committee: November 17, 2009 Dr Gerard Alberts Prof Dr Krzysztof Apt Prof Dr Dick de Jongh Prof Dr Benedikt Löwe Dr Elizabeth de Mol Dr Leen Torenvliet 1 “We are reaching the stage of development where each new gener- ation of participants is unaware both of their overall technological ancestry and the history of the development of their speciality, and have no past to build upon.” J.A.N. Lee in 1996 [73, p.54] “To many of our colleagues, history is only the study of an irrele- vant past, with no redeeming modern value –a subject without useful scholarship.” J.A.N. Lee [73, p.55] “[E]ven when we can't know the answers, it is important to see the questions. They too form part of our understanding. If you cannot answer them now, you can alert future historians to them.” M.S. Mahoney [76, p.832] “Only do what only you can do.” E.W. Dijkstra [103, p.9] 2 Abstract The history of computer science can be viewed from a number of disciplinary perspectives, ranging from electrical engineering to linguistics. As stressed by the historian Michael Mahoney, different `communities of computing' had their own views towards what could be accomplished with a programmable comput- ing machine. -
Turing's Influence on Programming — Book Extract from “The Dawn of Software Engineering: from Turing to Dijkstra”
Turing's Influence on Programming | Book extract from \The Dawn of Software Engineering: from Turing to Dijkstra" Edgar G. Daylight∗ Eindhoven University of Technology, The Netherlands [email protected] Abstract Turing's involvement with computer building was popularized in the 1970s and later. Most notable are the books by Brian Randell (1973), Andrew Hodges (1983), and Martin Davis (2000). A central question is whether John von Neumann was influenced by Turing's 1936 paper when he helped build the EDVAC machine, even though he never cited Turing's work. This question remains unsettled up till this day. As remarked by Charles Petzold, one standard history barely mentions Turing, while the other, written by a logician, makes Turing a key player. Contrast these observations then with the fact that Turing's 1936 paper was cited and heavily discussed in 1959 among computer programmers. In 1966, the first Turing award was given to a programmer, not a computer builder, as were several subsequent Turing awards. An historical investigation of Turing's influence on computing, presented here, shows that Turing's 1936 notion of universality became increasingly relevant among programmers during the 1950s. The central thesis of this paper states that Turing's in- fluence was felt more in programming after his death than in computer building during the 1940s. 1 Introduction Many people today are led to believe that Turing is the father of the computer, the father of our digital society, as also the following praise for Martin Davis's bestseller The Universal Computer: The Road from Leibniz to Turing1 suggests: At last, a book about the origin of the computer that goes to the heart of the story: the human struggle for logic and truth. -
A Biased History Of! Programming Languages Programming Languages:! a Short History Fortran Cobol Algol Lisp
A Biased History of! Programming Languages Programming Languages:! A Short History Fortran Cobol Algol Lisp Basic PL/I Pascal Scheme MacLisp InterLisp Franz C … Ada Common Lisp Roman Hand-Abacus. Image is from Museo (Nazionale Ramano at Piazzi delle Terme, Rome) History • Pre-History : The first programmers • Pre-History : The first programming languages • The 1940s: Von Neumann and Zuse • The 1950s: The First Programming Language • The 1960s: An Explosion in Programming languages • The 1970s: Simplicity, Abstraction, Study • The 1980s: Consolidation and New Directions • The 1990s: Internet and the Web • The 2000s: Constraint-Based Programming Ramon Lull (1274) Raymondus Lullus Ars Magna et Ultima Gottfried Wilhelm Freiherr ! von Leibniz (1666) The only way to rectify our reasonings is to make them as tangible as those of the Mathematician, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, in order to see who is right. Charles Babbage • English mathematician • Inventor of mechanical computers: – Difference Engine, construction started but not completed (until a 1991 reconstruction) – Analytical Engine, never built I wish to God these calculations had been executed by steam! Charles Babbage, 1821 Difference Engine No.1 Woodcut of a small portion of Mr. Babbages Difference Engine No.1, built 1823-33. Construction was abandoned 1842. Difference Engine. Built to specifications 1991. It has 4,000 parts and weighs over 3 tons. Fixed two bugs. Portion of Analytical Engine (Arithmetic and Printing Units). Under construction in 1871 when Babbage died; completed by his son in 1906. -
Church-Turing Thesis: Every Function F: {0,1}* -> {0,1}* Which Is "Effectively Computable" Is Computable by a Turing Machine
Church-Turing Thesis: Every function f: {0,1}* -> {0,1}* which is "effectively computable" is computable by a Turing Machine. Observation: Every Turing Machine (equivalently, every python program, or evey program in your favorite language) M can be encoded by a finite binary string #M. Moreover, our encoding guarantees #M != #M' whenever M and M' are different Turing Machines (different programs). Recall: Every finite binary string can be thought of as a natural number written in binary, and vice versa. Therefore, we can think of #M as a natural number. E.g. If #M = 1057, then we are talking about the 1057th Turing Machine, or 1057th python program. Intuitive takeaway: At most, there are as many different Turing Machines (Programs) as there are natural numbers. We will now show that some (in fact most) decision problems f: {0,1}* -> {0,1} are not computable by a TM (python program). If a decision problem is not comptuable a TM/program then we say it is "undecidable". Theorem: There are functions from {0,1}* to {0,1} which are not computable by a Turing Machine (We say, undecidable). Corollary: Assuming the CT thesis, there are functions which are not "effectively computable". Proof of Theorem: - Recall that we can think of instead of of {0,1}* - "How many" functions f: -> {0,1} are there? - We can think of each each such function f as an infinite binary string - For each x in (0,1), we can write its binary expansion as an infinite binary string to the right of a decimal point - The string to the right of the decimal point can be interpreted as a function f_x from natural numbers to {0,1} -- f_x(i) = ith bit of x to the right of the decimal point - In other words: for each x in (0,1) we get a different function f_x from natural numbers to {0,1}, so there are at least as many decision problems as there are numbers in (0,1). -
Computers Friday, February 12, 2021 11:00 AM
1 Introduction: Computers Friday, February 12, 2021 11:00 AM Welcome! CMSC 240 - Principles of Computer Organization Class website: https://cs.brynmawr.edu/Courses/cs240/Spring2021/ What is a computer? A device with • A processor (CPU - Central Processing Unit) • Storage/memory (RAM, Disk, USB Stick) • A keyboard • A mouse • A monitor • A printer Not all computers have all of the above. Except the CPU and memory. Japan's Fugaku Supercomputer is one of the world's fastest computer as of Summer 2020. Performance is over 400 petaflops (over a million times faster than the desktop shown on the right). Question: What was the first ever computer? 240 Lectures Page 1 1 Computers - Old & New Friday, February 12, 2021 11:00 AM The Difference Engine #2: A Mechanical Computer ENIAC Electronic Numerical Integrator and Computer February 15, 1946. ENIAC Day is this week! https://eniacday.org/ Check it out. Question: What is the difference between the ENIAC, the Apple Mac, the Iphone, and the Fugaku??? 240 Lectures Page 2 1 Turing Machines Friday, February 12, 2021 11:00 AM 1937: Alan M. Turing Turing Machine [A mathematical abstraction of mechanical computation.] Turing Machines for adding and multiplying Universal Turing Machine Church-Turing Thesis (tl;dr) Anything that can be computed can be computed by a Turing machine. Key Idea: A computer is essentially a Turing Machine. A computer is a universal computing device. 240 Lectures Page 3 1 Put on Watch List… Friday, February 12, 2021 8:55 AM 240 Lectures Page 4 1 von Neumann Architecture Friday, February 12, 2021 11:00 AM John von Neumann, 1945 Stored Program Computers Aka von Neumann Architecture Most computers today are based on this architecture. -
Universal Turing Machine
15-251 Great Theoretical Ideas in Computer Science Lecture 21 - Dan Kilgallin Turing Machines Goals Describe the nature of computation Mathematically formalize the behavior of a program running on a computer system Compare the capabilities of different programming languages Turing Machines What can we do to make a DFA better? Idea: Give it some memory! How much memory? Infinite! What kind of memory? Sequential access (e. g. CD, hard drive) or RAM? An infinite amount of RAM requires remembering really big numbers and needlessly complicates proofs Turing Machines: Definition A Turing Machine consists of A DFA to store the machine state, called the controller An array that is infinitely long in both directions, called the tape A pointer to some particular cell in the array, called the head Operation The head begins at cell 0 on the tape The DFA begins in some initial state Symbols from some alphabet are written on a finite portion of the tape, beginning at cell 1 Operation At each step, the machine uses as input: The state of the controller The symbol written on the cell which the head is at Using this, the machine will: Transition to some state in the DFA (possibly the same state) Write some symbol (possibly the same symbol) on the tape Move the head left or right one cell Two Flavors! The machine will stop computation if the DFA enters one of a pre-defined set of "halting" states A "decision" machine will, if it reaches a halting state, output either "Yes" or "No" (i.e. there are "accepting" and "rejecting" halt states) A "function" machine will, if it reaches a halting state, have some string of symbols written on the tape. -
Turing — the Father of Computer Science”
Towards a Historical Notion of \Turing | the Father of Computer Science" Third and last draft, submitted in August 2013 to the Journal History and Philosophy of Logic Edgar G. Daylight? Eindhoven University of Technology Department of Technology Management [email protected] Abstract. In the popular imagination, the relevance of Turing's the- oretical ideas to people producing actual machines was significant and appreciated by everybody involved in computing from the moment he published his 1936 paper `On Computable Numbers'. Careful historians are aware that this popular conception is deeply misleading. We know from previous work by Campbell-Kelly, Aspray, Akera, Olley, Priestley, Daylight, Mounier-Kuhn, and others that several computing pioneers, in- cluding Aiken, Eckert, Mauchly, and Zuse, did not depend on (let alone were they aware of) Turing's 1936 universal-machine concept. Further- more, it is not clear whether any substance in von Neumann's celebrated 1945 `First Draft Report on the EDVAC' is influenced in any identifiable way by Turing's work. This raises the questions: (i) When does Turing enter the field? (ii) Why did the Association for Computing Machin- ery (ACM) honor Turing by associating his name to ACM's most pres- tigious award, the Turing Award? Previous authors have been rather vague about these questions, suggesting some date between 1950 and the early 1960s as the point at which Turing is retroactively integrated into the foundations of computing and associating him in some way with the movement to develop something that people call computer science. In this paper, based on detailed examination of hitherto overlooked pri- mary sources, attempts are made to reconstruct networks of scholars and ideas prevalent to the 1950s, and to identify a specific group of ACM actors interested in theorizing about computations in computers and attracted to the idea of language as a frame in which to understand computation. -
Calculating Space) 1St
Konrad Zuse’s Rechnender Raum (Calculating Space) 1st. re-edition1 written in LATEX by A. German and H. Zenil As published in A Computable Universe: Understanding & Exploring Nature as Computation, World Scientific, 2012 Painting by Konrad Zuse (under the pseudonym “Kuno See”). Followed by an Afterword by Adrian German and Hector Zenil 2 1with kind permission by all parties involved, including MIT and Zuse’s family. 2The views expressed in the afterword do not represent the views of those organisations with which the authors are affiliated. 1 Calculating Space (“Rechnender Raum”)z Konrad Zuse Contents 1 INTRODUCTION 1 2 INTRODUCTORY OBSERVATIONS 3 2.1 Concerning the Theory of Automatons . .3 2.2 About Computers . .5 2.3 Differential Equations from the Point of View of the Automa- ton Theory . .8 2.4 Maxwell Equations . 10 2.5 An Idea about Gravitation . 13 2.6 Differential Equations and Difference Equations, Digitalization 13 2.7 Automaton Theory Observations of Physical Theories . 14 3 EXAMPLES OF DIGITAL TREATMENT OF FIELDS AND PARTICLES 19 3.1 The Expression “Digital Particle” . 19 3.2 Two-Dimensional Systems . 27 3.3 Digital Particles in Two-Dimensional Space . 30 3.4 Concerning Three-Dimensional Systems . 34 4 GENERAL CONSIDERATIONS 37 4.1 Cellular Automatons . 37 4.2 Digital Particles and Cellular Automatons . 39 4.3 On the Theory of Relativity . 39 zSchriften zur Datenverarbeitung, Vol. 1, 1969 Friedrich Vieweg & Sohn, Braun- schweig, 74 pp. MIT Technical TranslationTranslated for Massachusetts Institute of Tech- nology, Project MAC, by: Aztec School of Languages, Inc., Research Translation Division (164), Maynard, Massachusetts and McLean, Virginia AZT-70-164-GEMIT Massachusetts Institute of Technology, Project MAC, Cambridge, Massachusetts 02139—February 1970 2 4.4 Considerations of Information Theory . -
Pioneers of Computing
Pioneers of Computing В 1980 IEEE Computer Society учредило Золотую медаль (бронзовую) «Вычислительный Пионер» Пионерами учредителями стали 32 члена IEEE Computer Society, связанных с работами по информатике и вычислительным наукам. 1 Pioneers of Computing 1.Howard H. Aiken (Havard Mark I) 2.John V. Atanasoff 3.Charles Babbage (Analytical Engine) 4.John Backus 5.Gordon Bell (Digital) 6.Vannevar Bush 7.Edsger W. Dijkstra 8.John Presper Eckert 9.Douglas C. Engelbart 10.Andrei P. Ershov (theroretical programming) 11.Tommy Flowers (Colossus engineer) 12.Robert W. Floyd 13.Kurt Gödel 14.William R. Hewlett 15.Herman Hollerith 16.Grace M. Hopper 17.Tom Kilburn (Manchester) 2 Pioneers of Computing 1. Donald E. Knuth (TeX) 2. Sergei A. Lebedev 3. Augusta Ada Lovelace 4. Aleksey A.Lyapunov 5. Benoit Mandelbrot 6. John W. Mauchly 7. David Packard 8. Blaise Pascal 9. P. Georg and Edvard Scheutz (Difference Engine, Sweden) 10. C. E. Shannon (information theory) 11. George R. Stibitz 12. Alan M. Turing (Colossus and code-breaking) 13. John von Neumann 14. Maurice V. Wilkes (EDSAC) 15. J.H. Wilkinson (numerical analysis) 16. Freddie C. Williams 17. Niklaus Wirth 18. Stephen Wolfram (Mathematica) 19. Konrad Zuse 3 Pioneers of Computing - 2 Howard H. Aiken (Havard Mark I) – США Создатель первой ЭВМ – 1943 г. Gene M. Amdahl (IBM360 computer architecture, including pipelining, instruction look-ahead, and cache memory) – США (1964 г.) Идеология майнфреймов – система массовой обработки данных John W. Backus (Fortran) – первый язык высокого уровня – 1956 г. 4 Pioneers of Computing - 3 Robert S. Barton For his outstanding contributions in basing the design of computing systems on the hierarchical nature of programs and their data.