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| kruskal's tree theorem: Logic for Programming, Artificial Intelligence, and Reasoning Miki Hermann, Andrei Voronkov, 2006-10-23 This book constitutes the refereed proceedings of the 13th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2006, held in Phnom Penh, Cambodia in November 2006. The 38 revised full papers presented together with one invited talk were carefully reviewed and selected from 96 submissions. |
| kruskal's tree theorem: Rewriting Techniques and Applications Vincent van Oostrom, 2004-05-24 This book constitutes the refereed proceedings of the 15th International Conference on Rewriting Techniques and Applications, RTA 2004, held in Aachen, Germany in June 2004. |
| kruskal's tree theorem: Term Rewriting Systems Terese, 2003-03-20 Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations. |
| kruskal's tree theorem: Combinatorial Algebraic Geometry Aldo Conca, Sandra Di Rocco, Jan Draisma, June Huh, Bernd Sturmfels, Filippo Viviani, 2014-05-15 Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications. |
| kruskal's tree theorem: Certified Programs and Proofs Georges Gonthier, Michael Norrish, 2013-12-11 This book constitutes the refereed proceedings of the Third International Conference on Certified Programs and Proofs, CPP 2013, colocated with APLAS 2013 held in Melbourne, Australia, in December 2013. The 18 revised regular papers presented together with 1 invited lecture were carefully reviewed and selected from 39 submissions. The papers are organized in topical sections on code verification, elegant proofs, proof libraries, certified transformations and security. |
| kruskal's tree theorem: Reuniting the Antipodes - Constructive and Nonstandard Views of the Continuum Peter Schuster, Ulrich Berger, Horst Osswald, 2013-03-14 At first glance, Robinson's original form of nonstandard analysis appears nonconstructive in essence, because it makes a rather unrestricted use of classical logic and set theory and, in particular, of the axiom of choice. Recent developments, however, have given rise to the hope that the distance between constructive and nonstandard mathematics is actually much smaller than it appears. So the time was ripe for the first meeting dedicated simultaneously to both ways of doing mathematics – and to the current and future reunion of these seeming opposites. Consisting of peer-reviewed research and survey articles written on the occasion of such an event, this volume offers views of the continuum from various standpoints. Including historical and philosophical issues, the topics of the contributions range from the foundations, the practice, and the applications of constructive and nonstandard mathematics, to the interplay of these areas and the development of a unified theory. |
| kruskal's tree theorem: Types for Proofs and Programs Paul Callaghan, Zhaohui Luo, James McKinna, Robert Pollack, 2003-08-03 This book constitutes the thoroughly refereed post-proceedings of the International Workshop of the TYPES Working Group, TYPES 2000, held in Durham, UK in December 2000. The 15 revised full papers presented were carefully reviewed and selected during two rounds of refereeing and revision. All current issues on type theory and type systems and their applications to programming, systems design, and proof theory are addressed. |
| kruskal's tree theorem: Sets and Extensions in the Twentieth Century , 2012-01-24 Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights |
| kruskal's tree theorem: Handbook of Modal Logic Patrick Blackburn, Johan F.A.K. van Benthem, Frank Wolter, 2006-11-03 The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth |
| kruskal's tree theorem: Automata, Languages and Programming Kim G. Larsen, Sven Skyum, Glynn Winskel, 1998-07-06 This book constitutes the refereed proceedings of the 25th International Colloquium on Automata, Languages and Programming, ICALP'98, held in Aalborg, Denmark, in July 1998. The 70 revised full papers presented together with eight invited contributions were carefully selected from a total of 182 submissions. The book is divided in topical sections on complexitiy, verification, data structures, concurrency, computational geometry, automata and temporal logic, algorithms, infinite state systems, semantics, approximation, thorem proving, formal languages, pi-calculus, automata and BSP, rewriting, networking and routing, zero-knowledge, quantum computing, etc.. |
| kruskal's tree theorem: Exogenous Factors in Colonic Carcinogenesis W. Scheppach, M. Scheurlen, 2003-01-31 This book is the proceedings of Falk Symposium 128, held in Würzburg, Germany, on May 2-3, 2002, and dedicated to the important issue of colonic carcinogenesis and its underlying genetic and environmental factors. Colorectal cancer is one of the leading causes of cancer-related death in industrialized countries. It has been recognized to be the consequence of a dynamic process leading from hyperproliferative epithelium through different classes of adenomas to invasive carcinoma. This adenoma-carcinoma sequence has been characterized on a molecular basis. Modern molecular biology has also helped to clarify the clustering of colorectal cancer within families, a phenomenon that has been known to clinicians for a long time. Thus, the pathogenesis of the two distinct familial colon cancer syndromes FAP (familial adenomatous polyposis) and HNPCC (hereditary non-polyposis colorectal cancer) is increasingly being understood. Thereby, an identification of affected people has become possible before the disease has manifested. There is also convincing evidence that the pathogenesis of sporadic colonic cancer is modulated by environmental, mainly nutritional, factors. Carcinogens seem to be far less important than the components of the `normal' human diet. It is likely that the interplay between protective and noxious dietary compounds determines the progression of the adenoma-carcinoma sequence. Additionally, a broad spectrum of drugs has been shown to affect colonic tumorigenesis, which provides the rationale for chemoprevention strategies. These issues set the scene for discussions on how genetic and environmental factors may interact in the pathogenesis of colonic cancer, contributing fresh ideas to the prevention of this most prevalent malignancy in the industrialized world. |
| kruskal's tree theorem: Discrete Algebraic Methods Volker Diekert, Manfred Kufleitner, Gerhard Rosenberger, Ulrich Hertrampf, 2016-05-24 The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups |
| kruskal's tree theorem: Description Logic, Theory Combination, and All That Carsten Lutz, Uli Sattler, Cesare Tinelli, Anni-Yasmin Turhan, Frank Wolter, 2019-06-25 This Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that readers will enjoy the articles gathered in Franz's honour and appreciate the breadth and depth of his favourite areas of computer science. |
| kruskal's tree theorem: Handbook of Automated Reasoning Alan J.A. Robinson, Andrei Voronkov, 2001-06-21 Handbook of Automated Reasoning. |
| kruskal's tree theorem: The Multivariate Algorithmic Revolution and Beyond Hans L. Bodlaender, Rodney Downey, Fedor V. Fomin, Dániel Marx, 2012-06-16 Parameterized complexity is currently a thriving field in complexity theory and algorithm design. A significant part of the success of the field can be attributed to Michael R. Fellows. This Festschrift has been published in honor of Mike Fellows on the occasion of his 60th birthday. It contains 20 papers that showcase the important scientific contributions of this remarkable man, describes the history of the field of parameterized complexity, and also reflects on other parts of Mike Fellows’s unique and broad range of interests, including his work on the popularization of discrete mathematics for young children. The volume contains several surveys that introduce the reader to the field of parameterized complexity and discuss important notions, results, and developments in this field. |
| kruskal's tree theorem: Designing Reliable Distributed Systems Peter Csaba Ölveczky, 2018-02-12 This classroom-tested textbook provides an accessible introduction to the design, formal modeling, and analysis of distributed computer systems. The book uses Maude, a rewriting logic-based language and simulation and model checking tool, which offers a simple and intuitive modeling formalism that is suitable for modeling distributed systems in an attractive object-oriented and functional programming style. Topics and features: introduces classical algebraic specification and term rewriting theory, including reasoning about termination, confluence, and equational properties; covers object-oriented modeling of distributed systems using rewriting logic, as well as temporal logic to specify requirements that a system should satisfy; provides a range of examples and case studies from different domains, to help the reader to develop an intuitive understanding of distributed systems and their design challenges; examples include classic distributed systems such as transport protocols, cryptographic protocols, and distributed transactions, leader election, and mutual execution algorithms; contains a wealth of exercises, including larger exercises suitable for course projects, and supplies executable code and supplementary material at an associated website. This self-contained textbook is designed to support undergraduate courses on formal methods and distributed systems, and will prove invaluable to any student seeking a reader-friendly introduction to formal specification, logics and inference systems, and automated model checking techniques. |
| kruskal's tree theorem: Universal Algebra for Computer Scientists Wolfgang Wechler, 2012-12-06 A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers. |
| kruskal's tree theorem: Mathematical Foundations of Computer Science 2013 Krishnendu Chatterjee, Jirí Sgall, 2013-08-16 This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence. |
| kruskal's tree theorem: Ordinal Analysis with an Introduction to Proof Theory Toshiyasu Arai, 2020-08-11 This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed. |
| kruskal's tree theorem: CONCUR 2013 -- Concurrency Theory Pedro R. D'Argenio, Hernan Melgratti, 2013-07-23 This book constitutes the thoroughly refereed proceedings of the 24th International Conference on Concurrency Theory, CONCUR 2013, held in Buenos Aires, Argentina, August 27-30, 2013. The 34 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 115 submissions. The papers are organized in topics such as process semantics and modal transition systems, VAS and pushdown systems, Pi calculus and interaction nets, linearizability and verification of concurrent programs, verification of infinite models, model measure and reversibility, stochastic models, message-based interaction processes, principles of automatic verification, and games and control synthesis. |
| kruskal's tree theorem: Automata, Languages and Programming Michael S. Paterson, 1990 In subvolume 27C1 magnetic and related properties of binary lanthanide oxides have been compiled. This subvolume covers data obtained since 1980 and can therefore be regarded as supplement to volume III/12c. While in the previous volume the majority of magnetic data was obtained either from magnetometric measurements or from neutron diffraction, for the present data the main emphasis is devoted to 'related' properties without which, however, the understanding of classical magnetic properties is impossible. A second part 27C2 will deal with binary oxides of the actinide elements. |
| kruskal's tree theorem: Andrzej Mostowski and Foundational Studies A. Ehrenfeucht, Andrzej Ehrenfeucht, V.W. Marek, M. Srebrny, 2008-03-06 Andrzej Mostowski was one of the leading 20th century logicians. His legacy is examined in this volume of papers devoted both to his extraordinary scientific heritage and to the memory of him as a great researcher, teacher, organizer of science and human. Professor Mostowski pioneered and mastered many areas of mathematical logic. His contributions spanned set theory, recursion theory, and model theory - the backbone of foundations of mathematics. He is best known of the Kleene-Mostowski and Davis-Mostowski hierarchies of properties of integers reflecting the complexity of their definitions, and of the very elegant concept of a generalized quantifier which inspired and keeps stimulating a stream of deep work on fundamental issues of logics, deduction and reasoning both in mathematics and in computer science, and also of the contributions and excellent lectures on undecidability, unprovability, consistency and independence of various statements in set theory and arithmetic following Gödel, Tarski and Cohen. The overall content of the volume is designed to cover the current main streams in the field. For many years after WWII, especially in the late sixties, till his untimely death in 1975, Warsaw - where he led the centre of foundational studies - was a place where many leading logicians visited, studied, and started their career. Their memories form an important part of this volume, attempting to bring back the extraordinary achievements and personality of Mostowski. |
| kruskal's tree theorem: Verification of Data-Aware Processes via Satisfiability Modulo Theories Alessandro Gianola, 2023-10-29 This book is a revised version of the PhD dissertation written by the author at the Free University of Bozen-Bolzano in Italy. It presents a new approach to safety verification of a particular class of infinite-state systems, called Data-Aware Processes (DAPs). To do so, the developed technical machinery requires to devise novel results for uniform interpolation and its combination in the context of automated reasoning. These results are then applied to the analysis of concrete business processes enriched with real data. In 2022, the PhD dissertation won the “BPM Dissertation Award”, granted to outstanding PhD theses in the field of Business Process Management. |
| kruskal's tree theorem: Design and Implementation of Symbolic Computation Systems Alfonso Miola, 1990-03-26 The growing importance of the systems for symbolic computation has greatly influenced the decision of organizing DISCO '90 which is short for International Symposium on Design and Implementation of Symbolic Computation Systems. DISCO '90 focuses mainly on the most innovative methodological and technological aspects of hardware and software system design and implementation for Symbolic and Algebraic Computation, Automated Reasoning, Software Environments (Languages and User Interfaces), and Automatic Programming. In particular, it includes papers on the design and the development of significant running systems. The general objective of DISCO '90 is to present an up-to-date view of the field, while encouraging the scientific exchange among academic, industrial and user communities of the development of systems for symbolic computation. |
| kruskal's tree theorem: CRC Concise Encyclopedia of Mathematics Eric W. Weisstein, 2002-12-12 Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
| kruskal's tree theorem: Handbook Of Graph Grammars And Computing By Graph Transformations, Vol 2: Applications, Languages And Tools Grzegorz Rozenberg, 1999-10-20 Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact, within the area of graph grammars, graph transformation is considered as a fundamental computation paradigm where computation includes specification, programming, and implementation. Over the last three decades, graph grammars have developed at a steady pace into a theoretically attractive and important-for-applications research field.Volume 2 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations considers applications to functional languages, visual and object-oriented languages, software engineering, mechanical engineering, chemical process engineering, and images. It also presents implemented specification languages and tools, and structuring and modularization concepts for specification languages. The contributions have been written in a tutorial/survey style by the top experts in the corresponding areas. This volume is accompanied by a CD-Rom containing implementations of specification environments based on graph transformation systems, and tools whose implementation is based on the use of graph transformation systems. |
| kruskal's tree theorem: Handbook of Graph Grammars and Computing by Graph Transformation Hartmut Ehrig, 1997 Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others. The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact, within the area of graph grammars, graph transformation is considered a fundamental computation paradigm where computation includes specification, programming, and implementation. Over the last three decades, graph grammars have developed at a steady pace into a theoretically attractive and important-for-applications research field. Volume 2 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations considers applications to functional languages, visual and object-oriented languages, software engineering, mechanical engineering, chemical process engineering, and images. It also presents implemented specification languages and tools, and structuring and modularization concepts for specification languages. The contributions have been written in a tutorial/survey style by the top experts in the corresponding areas. This volume is accompanied by a CD-Rom containing implementations of specification environments based on graphtransformation systems, and tools whose implementation is based on the use of graph transformation systems. |
| kruskal's tree theorem: Automated Deduction – CADE-20 Robert Nieuwenhuis, 2005-07-14 This book constitutes the refereed proceedings of the 20th International Conference on Automated Deduction, CADE-20, held in Tallinn, Estonia, in July 2005. The 25 revised full papers and 5 system descriptions presented were carefully reviewed and selected from 78 submissions. All current aspects of automated deduction are addressed, ranging from theoretical and methodological issues to presentation and evaluation of theorem provers and logical reasoning systems. |
| kruskal's tree theorem: Kurt Gödel and the Foundations of Mathematics Matthias Baaz, Christos H. Papadimitriou, Hilary W. Putnam, Dana S. Scott, Charles L. Harper, Jr, 2011-06-06 This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers. |
| kruskal's tree theorem: Logic-Based Program Synthesis and Transformation Emanuele De Angelis, Wim Vanhoof, 2022-03-12 This book constitutes the refereed proceedings of the 31st International Conference on Logic-Based Program Synthesis and Transformation, LOPSTR 2021, which was held during September 7-8, 2021.* The 8 papers presented in this volume were carefully reviewed and selected from a total of 15 reviewed submissions. Additionally, the book also contains 1 full-length invited talk. *Conference was held as a hybrid event due to the COVID-19 pandemic. |
| kruskal's tree theorem: Programming Languages and Systems - Esop'96 Hanne R. Nielson, 1996-04-03 This book presents the refereed proceedings of the Sixth European Symposium on Programming, ESOP '96, held in Linköping, Sweden, in April 1996. The 23 revised full papers included were selected from a total of 63 submissions; also included are invited papers by Cliff B. Jones and by Simon L. Peyton Jones. The book is devoted to fundamental issues in the specification, analysis, and implementation of programming languages and systems; the emphasis is on research issues bridging the gap between theory and practice. Among the topics addressed are software specification and verification, programming paradigms, program semantics, advanced type systems, program analysis, program transformation, and implementation techniques. |
| kruskal's tree theorem: Parallel Computing Technologies Victor Malyshkin, 1997-08-06 This book constitutes the refereed proceedings of the Fourth International Conference on Parallel Computing Technologies, PaCT-97, held in Yaroslavl, Russia, in September 1997. The volume presents a total of 54 contributions: 21 full papers, 20 short papers, 10 posters, and three tutorials. All papers were selected for inclusion in the proceedings from numerous submissions on the basis of three independent reviews. The volume covers all current topics in parallel processing; it is divided into sections on theory, software, hardware and architecture, applications, posters, and tutorials. |
| kruskal's tree theorem: Surveys in Combinatorics 2015 Artur Czumaj, Agelos Georgakopoulos, Daniel Král, Vadim Lozin, Oleg Pikhurko, 2015-07-02 This volume contains nine survey articles based on the invited lectures given at the 25th British Combinatorial Conference, held at the University of Warwick in July 2015. This biennial conference is a well-established international event, with speakers from around the world. The volume provides an up-to-date overview of current research in several areas of combinatorics, including graph theory, Ramsey theory, combinatorial geometry and curves over finite fields. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of cutting-edge developments. The book provides a valuable survey of the present state of knowledge in combinatorics, and will be useful to researchers and advanced graduate students, primarily in mathematics but also in computer science and statistics. |
| kruskal's tree theorem: Impossible? Julian Havil, 2011-03-28 In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable—and all of it mathematically irrefutable. Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly—why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion—how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible? Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways. |
| kruskal's tree theorem: Rewriting Techniques and Applications Andrei Voronkov, 2008-07-11 This book constitutes the refereed proceedings of the 19th International Conference on Rewriting Techniques and Applications, RTA 2008, held in Hagenberg, Austria, July 15-17, in June 2008 as part of the RISC Summer 2008. The 30 revised full papers presented were carefully reviewed and selected from 57 initial submissions. The papers cover current research on all aspects of rewriting including typical areas of interest such as applications, foundational issues, frameworks, implementations, and semantics. |
| kruskal's tree theorem: If the Universe Is Teeming with Aliens ... WHERE IS EVERYBODY? Stephen Webb, 2015-05-18 Given the fact that there are perhaps 400 billion stars in our Galaxy alone, and perhaps 400 billion galaxies in the Universe, it stands to reason that somewhere out there, in the 14-billion-year-old cosmos, there is or once was a civilization at least as advanced as our own. The sheer enormity of the numbers almost demands that we accept the truth of this hypothesis. Why, then, have we encountered no evidence, no messages, no artifacts of these extraterrestrials? In this second, significantly revised and expanded edition of his widely popular book, Webb discusses in detail the (for now!) 75 most cogent and intriguing solutions to Fermi's famous paradox: If the numbers strongly point to the existence of extraterrestrial civilizations, why have we found no evidence of them? Reviews from the first edition: Amidst the plethora of books that treat the possibility of extraterrestrial intelligence, this one by Webb ... is outstanding. ... Each solution is presented in a very logical, interesting, thorough manner with accompanying explanations and notes that the intelligent layperson can understand. Webb digs into the issues ... by considering a very broad set of in-depth solutions that he addresses through an interesting and challenging mode of presentation that stretches the mind. ... An excellent book for anyone who has ever asked ‘Are we alone?’. (W. E. Howard III, Choice, March, 2003) Fifty ideas are presented ... that reveal a clearly reasoned examination of what is known as ‘The Fermi Paradox’. ... For anyone who enjoys a good detective story, or using their thinking faculties and stretching the imagination to the limits ... ‘Where is everybody’ will be enormously informative and entertaining. ... Read this book, and whatever your views are about life elsewhere in the Universe, your appreciation for how special life is here on Earth will be enhanced! A worthy addition to any personal library. (Philip Bridle, BBC Radio, March, 2003) Since gaining a BSc in physics from the University of Bristol and a PhD in theoretical physics from the University of Manchester, Stephen Webb has worked in a variety of universities in the UK. He is a regular contributor to the Yearbook of Astronomy series and has published an undergraduate textbook on distance determination in astronomy and cosmology as well as several popular science books. His interest in the Fermi paradox combines lifelong interests in both science and science fiction. |
| kruskal's tree theorem: Automata, Languages and Programming Luca Aceto, Monika Henzinger, Jiri Sgall, 2011-06-21 The two-volume set LNCS 6755 and LNCS 6756 constitutes the refereed proceedings of the 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, held in Zürich, Switzerland, in July 2011. The 114 revised full papers (68 papers for track A, 29 for track B, and 17 for track C) presented together with 4 invited talks, 3 best student papers, and 3 best papers were carefully reviewed and selected from a total of 398 submissions. The papers are grouped in three major tracks on algorithms, complexity and games; on logic, semantics, automata, and theory of programming; as well as on foundations of networked computation: models, algorithms and information management. |
| kruskal's tree theorem: Mathematics of Program Construction Johan Jeuring, 1998-05-27 This book consitutes the refereed proceedings of the 4th International Conference on Mathematics of Program Construction, MPC'98, held in Marstrand, near Goteborg, Sweden, in June 1998. The 17 revised full papers presented were selected from 57 submissions; also included are three invited contributions. The volume is devoted to the use of crisp, clear mathematics in the discovery and design of algorithms and in the development of corresponding software and hardware; varoius approaches to formal methods for systems design and analysis are covered. |
| kruskal's tree theorem: The Biggest Number in the World David Darling, Agnijo Banerjee, 2022-05-05 From cells in our bodies to measuring the universe, big numbers are everywhere We all know that numbers go on forever, that you could spend your life counting and never reach the end of the line, so there can’t be such a thing as a ‘biggest number’. Or can there? To find out, David Darling and Agnijo Banerjee embark on an epic quest, revealing the answers to questions like: are there more grains of sand on Earth or stars in the universe? Is there enough paper on Earth to write out the digits of a googolplex? And what is a googolplex? Then things get serious. Enter the strange realm between the finite and the infinite, and float through a universe where the rules we cling to no longer apply. Encounter the highest number computable and infinite kinds of infinity. At every turn, a cast of wild and wonderful characters threatens the status quo with their ideas, and each time the numbers get larger. |
| kruskal's tree theorem: Formal Models and Semantics Bozzano G Luisa, 2014-06-28 The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing. |
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