This is the most comprehensive treatment available in book form of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. A revealing analysis of the natural order of decidable and undecidable cases is given. The complete classification of the solvable and unsolvable standard cases of the classical decision problem will be of particular interest to the reader. The classification comes complete with the complexity analysis of the solvable cases, with the comprehensive treatment of the reduction method, and with the model-theoretical analysis of solvable cases. Many cases are treated here for the first time, and a great number of simple proofs and exercises have been included. The results and methods of the book are extensively used in logic, computer science and artificial intelligence.

This book constitutes the refereed proceedings of the International Seminar on Proof Theory in Computer Science, PTCS 2001, held in Dagstuhl Castle, Germany, in October 2001.The 13 thoroughly revised full papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are higher type recursion, lambda calculus, complexity theory, transfinite induction, categories, induction-recursion, post-Turing analysis, natural deduction, implicit characterization, iterate logic, and Java programming.

As society comes to rely increasingly on software for its welfare and prosperity there is an urgent need to create systems in which it can trust. Experience has shown that confidence can only come from a more profound understanding of the issues, which in turn can come only if it is based on logically sound foundations.
This volume contains contributions from leading researchers in the critical disciplines of computing and information science, mathematics, logic, and complexity. All contributions are self-contained, aiming at comprehensibility as well as comprehensiveness. The volume also contains introductory hints to technical issues, concise surveys, introductions, and various fresh results and new perspectives.

This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001.The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

This volume contains the proceedings of the 22nd International Conference on Application and Theory of Petri Nets. The aim of the Petri net conferences is to create a forum for discussing progress in the application and theory of Petri nets. Typically, the conferences have 100{150 participants { one third of these coming from industry while the rest are from universities and research institutions. The conferences always take place in the last week of June. This year the conference was organized jointly with the 2nd International Conference on Application of Concurrency to System Design (ICACSD 2001). The two conferences shared the invited lectures and the social program. The conference and a number of other activities are co-ordinated by a steering committee with the following members: G. Balbo (Italy), J. Billington (Aust- lia), G. De Michelis (Italy), C. Girault (France), K. Jensen (Denmark), S. - magai (Japan), T. Murata (USA), C.A. Petri (Germany; honorary member), W. Reisig (Germany), G. Rozenberg (The Netherlands; chairman), and M. Silva (Spain). Other activities before and during the 2001 conference included tool dem- strations, a meeting on \XML Based Interchange Formats for Petri Nets," - tensive introductory tutorials, two advanced tutorials on \Probabilistic Methods in Concurrency" and \Model Checking," and two workshops on \Synthesis of Concurrent Systems" and \Concurrency in Dependable Computing." The tu- rial notes and workshop proceedings are not published in these proceedings, but copies are available from the organizers.

This book constitutes the refereed proceedings of the 5th International Conference on Typed Lambda Calculi and Applications, TLCA 2001, held in Krakow, Poland in May 2001. The 28 revised full papers presented were carefully reviewed and selected from 55 submissions. The volume reports research results on all current aspects of typed lambda calculi. Among the topics addressed are type systems, subtypes, coalgebraic methods, pi-calculus, recursive games, various types of lambda calculi, reductions, substitutions, normalization, linear logic, cut-elimination, prelogical relations, and mu calculus.

This book constitutes the thoroughly refereed post-proceedings of the 6th International Workshop on DNA-Based Computers, DNA 2000, held in Leiden, The Netherlands, in June 2000.The 16 revised full papers presented together with two invited papers were carefully reviewed and selected from 33 submissions. All current aspects of DNA computing, ranging from theoretical and foundational issues to algorithms, are addressed, from the computer science point of view as well as from the molecular biology point of view.

Stat Labs: Mathematical Statistics Through Applications blends mathematical statistics with modern statistical practice. It turns the traditional teaching of mathematical statistics on its head by making a case study the centerpiece of each chapter. Chapters begin with the introduction of a real problem followed by a description of the data collected to address the problem, rich background material to put the problem in context, and suggestions for investigating the problem. This novel approach to bringing data analysis into the theoretical course is ideal for motivating and illustrating standard statistical techniques, for helping students understand mathematical statistics, and for showing how statistics can be useful in a wide variety of contexts. Stat Labs is designed for use in a calculus-based introductory statistics course. It would be equally effective as a stand-alone text or as a supplement to a traditional mathematical statistics text. Deborah Nolan received her Ph.D in Statistics from Yale University, and she is now Professor of Statistics at the University of California, Berkeley. Her research interests include high-dimensional modeling, the teaching of statistics, and the use of technology in education. She has also been involved in encouraging women into research careers in the mathematical sciences, and in 1997 edited the volume, Women in Mathematics: Scaling the Heights for the Mathematical Association of America. Terry Speed's professional activities center around teaching and research involving th application of statistics to genetics and molecular biology. He spends 50% of his time in the Department of Statistics of the University of California at Berkeley, and the other 50% with the Genetics and Bioinformatics Group of the Walter & Eliza Hall Institute of Medical Research in Melbourne, Australia.

This book constitutes the thoroughly refereed post-workshop proceedings of the 15th International Workshop on Algebraic Development Techniques, WADT 2001, held jointly with the General Workshop of the ESPRIT Working Group CoFI in Genova, Italy, in April 2001.The book presents 16 papers selected from 32 workshop presentations. Among the topics addressed are formal specification, specification languages, term rewriting, and proof systems.

This book covers blockchain from the underlying principles to how it enables applications to survive and surf on its shoulder. Having covered the fundamentals of blockchain, the book turns to cryptocurrency. It thoroughly examines Bitcoin before presenting six other major currencies in a rounded discussion. The book then bridges between technology and finance, concentrating on how blockchain-based applications, including cryptocurrencies, have pushed hard against mainstream industries in a bid to cement their positions permanent. It discusses blockchain as underlying banking technology, crypto mining and offering, cryptocurrency as investment instruments, crypto regulations, and markets.

This volumecontains the papers presentedatthe SeventhInternationalC- ference on Logicfor Programmingand Automated Reasoning (LPAR 2000)held onReunionIsland, France,6 10November2000, followedbythe ReunionWo- shop on Implementation of Logic. Sixty-?ve papers were submitted to LPAR 2000 of which twenty-six papers were accepted. Submissions by the program committee members were not - lowed. There was a special category of experimental papers intended to describe implementations of systems, to report experiments with implemented systems, orto compareimplementedsystems.Eachof thesubmissionswasreviewedbyat least three program committee members and an electronic program committee meeting was held via the Internet. In addition to the refereed papers, this volume contains full papers by two of the four invited speakers, Georg Gottlob and Micha] el Rusinowitch, along with an extended abstract of Bruno Courcelle s invited lecture and an abstract of Erich Gr] adel s invited lecture. WewouldliketothankthemanypeoplewhohavemadeLPAR2000possible. We are grateful to the following groups and individuals: the program and or- nizing committees; the additional referees; the local arrangements chair Teodor Knapik; PascalManoury, who was in chargeof accommodation; Konstantin - rovin, whomaintainedthe programcommittee Webpage;andBillMcCune, who implemented the program committee management software."

This book contains all full papers presented at ACRI 2000, the Fourth International Conference on Cellular Automata for Research and Industry, held at the University of Karlsruhe (Germany), 4 - 6 October, 2000. The continuation of and growing interest in research on Cellular Automata models for real world phenomena indicates the feasibility of this approach. A quick glance at the table contents of this book shows that results came from such different areas as biology, economics, physics, traffic flow and urban development. This work is complemented by contributions on the implementation and evaluation of software for Cellular Automata simulation, which is a necessary (but of course in no way sufficient) ingredient for the successful application of Cellular Automata. Applying Cellular Automata without trying to understand their behavior, in depth would be an unfortunate development. But as properties and power in earlier years it was again one of the strong points of ACRI to bring together researchers not only from different application areas but also from theory. Of course, this is reflected by the list of accepted contributions which also comprise theoretical papers and even papers which certainly belong to the intersection of several fields. Examples are the generation and recognition of geometrical patters and the influence of possible failures on the power of CA which obviously are of relevance also to applications.

This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.

Are mathematical equations the best way to model nature? For many years it had been assumed that they were. But in the early 1980s, Stephen Wolfram made the radical proposal that one should instead build models that are based directly on simple computer programs. Wolfram made a detailed study of a class of such models known as cellular automata, and discovered a remarkable fact: that even when the underlying rules are very simple, the behavior they produce can be highly complex, and can mimic many features of what we see in nature. And based on this result, Wolfram began a program of research to develop what he called ?A Science of Complexity.?The results of Wolfram's work found many applications, from the so-called Wolfram Classification central to fields such as artificial life, to new ideas about cryptography and fluid dynamics. This book is a collection of Wolfram's original papers on cellular automata and complexity. Some of these papers are widely known in the scientific community; others have never been published before. Together, the papers provide a highly readable account of what has become a major new field of science, with important implications for physics, biology, economics, computer science and many other areas.

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: * Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts * Numerous examples that illustrate theorems and employ basic concepts such as Euclid s lemma, the Fibonacci sequence, and unique factorization * Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Lowenheim Skolem, Burali-Forti, Hartogs, Cantor Schroder Bernstein, and Konig An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

This volume contains the proceedings of FroCoS2000, the 3rd International WorkshoponFrontiersofCombiningSystems, heldMarch22-24,2000, inNancy, France. Like its predecessors organized in Munich (1996) and in Amsterdam (1998), FroCoS2000 is intended to o?er a common forum for research activities related to the combination and the integration of systems in the areas of logic, automateddeduction, constraintsolving, declarativeprogramming, andarti?cial intelligence. There were 31 submissions of overall high quality, authored by researchers from countries including Australia, Brasil, Belgium, Chili, France, Germany, - pan, Ireland, Italy, Portugal, Spain, Switzerland, The Netherlands, the United Kingdom, and the United States of America. All submissions were thoroughly evaluatedonthebasisofatleastthreerefereereports, andanelectronicprogram committeemeetingwasheldthroughtheInternet.Theprogramcommitteesel- ted 14 research contributions. The topics covered by the selected papers include: combinationoflogics;combinationofconstraintsolvingtechniques, combination of decision procedures; modular properties for theorem proving; combination of deduction systems and computer algebra; integration of decision procedures and other solving processes into constraint programming and deduction systems. We welcomed ?ve invited lectures by Alexander Bockmayr on "Combining Logic and Optimization in Cutting Plane Theory," Gilles Dowek on "Axioms vs. Rewrite Rules: From Completeness to Cut Elimination," Klaus Schulz on "Why Combined Decision Problems Are Often Intractable," Tomas Uribe on "Combinations of Theorem Proving and Model Checking," and Richard Zippel on "Program Composition Techniques for Numerical PDE Codes." Full papers of these lectures, except the last one, are also included in this volume.

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

This book comprises revised full versions of lectures given during the 9th European Summer School in Logic, Languages, and Information, ESSLLI'97, held in Aix-en-Provence, France, in August 1997. The six lectures presented introduce the reader to the state of the art in the area of generalized quantifiers and computation. Besides an introductory survey by the volume editor various aspects of generalized quantifiers are studied in depth.

Cryptology: Classical and Modern, Second Edition proficiently introduces readers to the fascinating field of cryptology. The book covers classical methods including substitution, transposition, Alberti, Vigenere, and Hill ciphers. It also includes coverage of the Enigma machine, Turing bombe, and Navajo code. Additionally, the book presents modern methods like RSA, ElGamal, and stream ciphers, as well as the Diffie-Hellman key exchange and Advanced Encryption Standard. When possible, the book details methods for breaking both classical and modern methods. The new edition expands upon the material from the first edition which was oriented for students in non-technical fields. At the same time, the second edition supplements this material with new content that serves students in more technical fields as well. Thus, the second edition can be fully utilized by both technical and non-technical students at all levels of study. The authors include a wealth of material for a one-semester cryptology course, and research exercises that can be used for supplemental projects. Hints and answers to selected exercises are found at the end of the book. Features: Requires no prior programming knowledge or background in college-level mathematics Illustrates the importance of cryptology in cultural and historical contexts, including the Enigma machine, Turing bombe, and Navajo code Gives straightforward explanations of the Advanced Encryption Standard, public-key ciphers, and message authentication Describes the implementation and cryptanalysis of classical ciphers, such as substitution, transposition, shift, affine, Alberti, Vigenere, and Hill

The papers contained in this volume were presented at the third international Workshop on Implementing Automata, held September 17{19,1998, at the U- versity of Rouen, France. Automata theory is the cornerstone of computer science theory. While there is much practical experience with using automata, this work covers diverse - eas, includingparsing, computationallinguistics, speechrecognition, textsear- ing, device controllers, distributed systems, andprotocolanalysis.Consequently, techniques that have been discovered in one area may not be known in another. In addition, there is a growing number of symbolic manipulation environments designed to assist researchers in experimenting with and teaching on automata and their implementation; examples include FLAP, FADELA, AMORE, Fire- Lite, Automate, AGL, Turing's World, FinITE, INR, and Grail. Developers of such systems have not had a forum in which to expose and compare their work. The purpose of this workshop was to bring together members of the academic, research, andindustrialcommunitieswithaninterestinimplementingautomata, to demonstrate their work and to explain the problems they have been solving. These workshops started in 1996 and 1997 at the University of Western Ontario, London, Ontario, Canada, prompted by Derick Wood and Sheng Yu. The major motivation for starting these workshops was that there had been no single forum in which automata-implementation issues had been discussed. The interest shown in the r st and second workshops demonstrated that there was a need for such a forum. The participation at the third workshop was very interesting: we counted sixty-three registrations, four continents, ten countries, twenty-three universities, and three companie

A First Course in Logic is an introduction to first-order logic suitable for first and second year mathematicians and computer scientists. There are three components to this course: propositional logic; Boolean algebras; and predicate/first-order, logic. Logic is the basis of proofs in mathematics - how do we know what we say is true? - and also of computer science - how do I know this program will do what I think it will? Surprisingly little mathematics is needed to learn and understand logic (this course doesn't involve any calculus). The real mathematical prerequisite is an ability to manipulate symbols: in other words, basic algebra. Anyone who can write programs should have this ability.

Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods." This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.

"Deduction" is an efficient and elegant presentation of classical first-order logic. It presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague. Both are very natural and easy to learn. The definition of a formula excludes free variables, and the deduction system uses "Show" lines; the combination allows rules to be stated very simply.

The book's main innovation is its final part, which contains chapters on extensions and revisions of classical logic: modal logic, many-valued logic, fuzzy logic, intuitionistic logic, counterfactuals, deontic logic, common-sense reasoning, and quantified modal logic. These have been areas of great logical and philosophical interest over the past 40 years, but few other textbooks treat them in any depth. "Deduction" makes these areas accessible to introductory students. All chapters have discussions of the underlying semantics and present both truth tree and deduction systems.

New features in this edition, in addition to truth tree systems for classical and nonclassical logics, include new and simpler rules for modal logic, deontic logic, and counterfactuals; discussions of many-valued, fuzzy, and intuitionistic logics; an introduction to common-sense reasoning (nonmonotonic logic); and extensively reworked problem sets, designed to lead students gradually from easier to more difficult problems. This new edition also features web-based programs that make use of the book's methods. Each program is set up to give students symbolization problems, give them hints, grade their work, and do problems for them.

The 1998Annual Conference of the EuropeanAssociation for Computer Science Logic, CSL'98, was held in Brno, Czech Republic, during August 24-28, 1998. CSL'98wasthe12thinaseriesofworkshopsandthe7thtobeheldasthe Annual Conference of the EACSL. The conference was organized at Masaryk University in Brno by the Faculty of Informatics in cooperation with universities in Aaachen, Caen, Haagen, Linz, Metz, Pisa, Szeged, Vienna, and other institutions. CSL'98 formed one part of a federated conferences event, the other part being MFCS'98, the 23rd Int- national Symposium on the Mathematical Foundations of Computer Science. This federated conferences event consisted of common plenary sessions, invited talks, several parallel technical programme tracks, a dozen satellite workshops organized in parallel, and tutorials. The Federated CSL/MFCS'98 Conferences event included 19 invited talks, four of them joint CSL/MFCS'98 talks (D. Harel, W. Maass, Y. Matiyasevic, and M. Yannakakis), four for CSL (P. Hajek, J. Mitchell, Th. Schwentick, and J. Tiuryn), and eleven for MFCS. Last but not least, two tutorials were organized by CSL on the day preceding the symposium on "Inference Rules in Fragments of Arithmetic" by Lev Beklemishev and on "Proofs, Types, and Safe Mobile Code" by Greg Morrisett. A total of 345 persons attended the Federated CSL/MFCS'98 Conference which was a great success. The program committee of CSL'98 selected 27 of 74 papers submitted for the conference.From the 27 papers selected for presentation,25 havebeen accepted, following the standard refereeeing procedure, for publication in the present p- ceedings. Three invited speakers submitted papers, that were likewise refereeed and accepted.