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Value-Range Analysis of C Programs : Towards Proving the Absence of Buffer Overflow Vulnerabilities
The use of static analysis techniques to prove the partial correctness of C code has recently attracted much attention due to the high cost of software errors - particularly with respect to security vulnerabilities. However, research into new analysis techniques is often hampered by the technical difficulties of analysing accesses through pointers, pointer arithmetic, coercion between types, integer wrap-around and other low-level behaviour. Axel Simon provides a concise, yet formal description of a value-range analysis that soundly approximates the semantics of C programs using systems of linear inequalities (polyhedra). The analysis is formally specified down to the bit-level while providing a precise approximation of all low-level aspects of C using polyhedral operations and, as such, it provides a basis for implementing new analyses that are aimed at verifying higher-level program properties precisely. One example of such an analysis is the tracking of the NUL position in C string buffers, which is shown as an extension to the basic analysis and which thereby demonstrates the modularity of the approach.
Tropical Algebraic Geometry
Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties.These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject.
Towards Mechanized Mathematical Assistants ; 14th Symposium, Calculemus 2007, 6th International Conference, MKM 2007, Hagenberg, Austria, June 27-30, 2007, Proceedings
Contains the collected contributions of two conferences, Calculemus 2007 and MKM 2007. Calculemus 2007 was the 14th in a series of conferences dedicated to the integration of computer algebra systems (CAS) and automated deduction systems (ADS). MKM 2007 was the sixth International Conference on Mathematical Knowledge Management, an emerging interdisciplinary field of research in the intersection of mathematics, computer science, library science, and scientific publishing. Both conferences aimed to provide mechanized mathematical assistants. Although the two conferences have separate communities and separate foci, there is a signi?cant overlap in the interests in building mechanized mathematical assistants. For this reason it was decided to collocate the two events in 2007 for the first time, at RISC in Hagenberg, Austria.
Topics in the Theory of Algebraic Function Fields
This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers.
Topics in Galois Fields
Provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm.
Theory of Association Schemes
Presents treatment of the structure theory of association schemes. This book presents generalization of Sylow's group theoretic theorems to scheme theory and also the algebraic proof of Tits' theorem on buildings of spherical type. It also includes characterization of Glauberman's, Z-involutions and is aimed at advanced undergraduate students
Theory and Applications of Satisfiability Testing ; Vol. 3569 ; 8th International Conference, SAT 2005, St Andrews, Scotland, June 19-23, 2005, Proceedings
SAT is the classic problem of determining whether or not a propositional formula has a satisfying truth assignment. It was the first problem shown by Cook to be NP-complete. Despite its seemingly specialized nature, satisfiability testing has proved to extremely useful in a wide range of different disciplines, both from a practical as well as from a theoretical point of view. For example, work on SAT continues to provide insight into various fundamental problems in computation, and SAT solving technology has advanced to the point where it has become the most effective way of solving a number of practical problems. The SAT series of conferences are multidisciplinary conferences intended to bring together researchers from various disciplines who are interested in SAT. Topics of interest include, but are not limited to: proof systems and proof c- plexity; search algorithms and heuristics; analysis of algorithms; theories beyond the propositional; hard instances and random formulae; problem encodings; - dustrial applications; solvers and other tools.
Theory and Applications of Ordered Fuzzy Numbers : A Tribute to Professor Witold Kosiński
This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.
The Universe in a Handkerchief : Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays
This book contains scores of intriguing puzzles and paradoxes from Lewis Carroll, the author of Alice in Wonderland, whose interests ranged from inventing new games like Arithmetical Croquet to important problems in symbolic logic and propositional calculus. Written by Carroll expert and well-known mathematics author Martin Gardner, this tour through Carroll's inventions is both fun and informative.
The shaping of arithmetic after C.F. Gausss disquisitiones arithmeticae
Traces the profound effect Gauss’s masterpiece has had on mathematics over the past two centuries. … The shaping of arithmetic is a major accomplishment, one which will stand as an important reference work on the history of number theory for many years.The editors and authors deserve our thanks for their efforts."It’s a big book, with eighteen authors and almost six hundred pages, and it mixes the work of well-established scholars with that of recent Ph.D.’s.
The Mathematica GuideBook for Numerics
Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility.The available types of arithmetic (machine, high-precision, and interval) are introduced, discussed, and put to use. Fundamental numerical operations, such as compiling programs, fast Fourier transforms, minimization, numerical solution of equations, ordinary/partial differential equations are analyzed in detail and are applied to a large number of examples in the main text and solutions to the exercises.
The Map of My Life
In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.
The Legacy of Mario Pieri in Geometry and Arithmetic
The Italian mathematician Mario Pieri (1860-1913) played an integral part in the research groups of Corrado Segre and Giuseppe Peano, and thus had a significant, yet somewhat underappreciated impact on several branches of mathematics, particularly on the development of algebraic geometry and the foundations of mathematics in the years around the turn of the 20th century. This book is the first in a series of three volumes that are dedicated to countering that neglect and comprehensively examining Pieri’s life, mathematical work, and influence in such diverse fields as mathematical logic, algebraic geometry, number theory, inversive geometry, vector analysis, and differential geometry.
The Last Recreations : Hydras, Eggs, and Other Mathematical Mystifications
Of all of Martin Gardner's writings, none gained him a wider audience or was more central to his reputation than his Mathematical Recreations column in "Scientific American", which virtually defined the genre of popular mathematics writing for a generation. Flatland, Hydras and Eggs: Mathematical Mystifications will be the final collection of these columns, covering a period roughly from 1979 to Gardner's retirement as a regular columnist in 1986. The notable trend over Gardner's career is the increasing sophistication of the mathematics he has been able to translate into his famously lucid prose. These columns show him at the top of his form and are not to be missed by anyone with an interest in mathematics. As always in his published collections, Gardner includes letters received from mathematicians and other commenting on the ideas presented in the columns.
The Calculus of Computation : Decision Procedures with Applications to Verification
Computational logic is a fast-growing field with applications in artificial intelligence, constraint solving, and the design and verification of software and hardware systems. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. This textbook also presents a logical approach to engineering correct software. The increasing ubiquity of computers makes implementing correct systems more important than ever. Verification exercises develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems.
The brain : Fuzzy arithmetic to quantum computing
The Brain- From Fuzzy Arithmetic to Quantum Computing" presents an original and astounding new understanding of the brain by taking into account novel achievements in Fuzziness and Quantum Information Theory. Bringing together Neuroscience, Soft Computing, Quantum Theory, and recent developments in mathematics the actual knowledge about the brain functioning is formalized into a coherent theoretical framework. This monograph develops new and powerful neural models providing formal descriptions of biochemical transactions in the brain to guide neuroscience experiments and to better interpret their results. This book demonstrates how the physiology of the neuron can be understood based on the fundamentals of fuzzy formal languages and introduces the basics of quantum computation and quantum information to the brain.intelligent system.
The Arché Papers on the Mathematics of Abstraction
Collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. the present volume is unique in presenting a thorough going examination of the mathematical aspects of the neo-logicist project (and the particular philosophical issues arising from these technical concerns). Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut - or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies. As a result, the volume provides a test of the scope and limits of the neo-logicist project, detailing what has been accomplished and outlining the desiderata still outstanding.
RP2040 Assembly Language Programming : ARM Cortex-M0+ on the Raspberry Pi Pico
Learn to program the Raspberry Pi Pico’s dual ARM Cortex M0+ CPUs in Assembly Language. The Pico contains a customer System on a Chip (SoC) called the RP2040, making it the Foundation’s first entry into the low-cost microcontroller market. The RP2040 contains a wealth of coprocessors for performing arithmetic as well as performing specialized I/O functionality. This book will show you how these CPUs work from a low level, easy-to-learn perspective. You will: Read and understand the Assembly Language code that is part of the Pico’s SDK Integrate Assembly Language and C code together into one program Interface to available options for DIY electronics and IoT projects
Reliable Implementation of Real Number Algorithms; Theory and Practice ; International Seminar Dagstuhl Castle, Germany, January 8-13, 2006 Revised Papers
The book was inteded to stimulate an exchange of ideas between the different communities that deal with the problem of reliable implementation of real number algorithms. Topics included formal proofs, software libraries, systems and platforms, as well as computational geometry and solid modelling.
Recent Advances in Parallel Virtual Machine and Message Passing Interface ; 15th European PVM/MPI Users’ Group Meeting, Dublin, Ireland, September 7-10, 2008. Proceedings
This book is organized in topical sections on applications, collective operations, library internals, message passing for multi-core and mutlithreaded architectures, MPI datatypes, MPI I/O, synchronisation issues in point-to-point and one-sided communications, tools, and verification of message passing programs.
