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In ordinary mathematics, an equation can be written down which is syntactically correct, but for which no solution exists. For example, consider the equation x = x + 1 defined over the real numbers; there is no value of x which satisfies it. Similarly it is possible to specify objects using the formal specification language Z [3,4], which can not possibly exist. Such specifications are called inconsistent and can arise in a number of ways. Example 1 The following Z specification of a functionf, from integers to integers "f x : ~ 1 x ~ O· fx = x + 1 (i) "f x : ~ 1 x ~ O· fx = x + 2 (ii) is inconsistent, because axiom (i) gives f 0 = 1, while axiom (ii) gives f 0 = 2. This contradicts the fact that f was declared as a function, that is, f must have a unique result when applied to an argument. Hence no suchfexists. Furthermore, iff 0 = 1 andfO = 2 then 1 = 2 can be deduced! From 1 = 2 anything can be deduced, thus showing the danger of an inconsistent specification. Note that all examples and proofs start with the word Example or Proof and end with the symbol.1.
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The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.
Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.
Work with data like a pro using this guide that breaks down how to organize, apply, and most importantly, understand what you are analyzing in order to become a true data ninja. From the stock market to genomics laboratories, census figures to marketing email blasts, we are awash with data. But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models—from linear regression to random walks and far beyond—that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.
C. Amting Directorate General Information Society, European Commission, Brussels Under the 4th Framework of European Research, the European Systems and Soft ware Initiative (ESSI) was part of the ESPRIT Programme. This initiative funded more than 470 projects in the area' of software and system process improvements. The majority of these projects were process improvement experiments carrying out and taking up new development processes, methods and technology within the software development process of a company. In addition, nodes (centres of exper tise), European networks (organisations managing local activities), training and dissemination actions complemented the process improvement experi...
Online Matchmaking examines the joys, fears, and disappointments of hooking up with people in cyberspace. Unlike many other books in the field, this collection includes studies by experts from a range of disciplines including Communications, Cultural Studies, Health, Journalism, Psychology, Rhetoric, and Sociology.
This book presents a comprehensive international overview of software quality assurance and metrics practice with contributions from around the world. The combination of the international perspective and practical case studies presented here will make this book invaluable to all practitioners and students in software engineering.
"In twenty two chapters, When We Ruled examines the nature of what we call Black history; critically surveying the often-shoddy documentation of that history. Importantly, it focuses upon African civilization in the Valley of the Nile and analyzes the key historical phases of Ancient Egypt--critical exercises for any professed scholar of African history and vital pieces of Africa's legacy ... When we Ruled is a timely and immensely important work of benefit to scholars and students alike. I am proud to add it to my library, from the Introduction--Runoko Rashidi. Available for the first time in paperback, this edition includes over 100 images, 18 maps, a 15 page chronological table, index, and bibliography. New introduction by Runoko Rashidi for the Black Classic Press edition."--Amazon.com.