This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.

This book constitutes the refereed proceedings of the 16th International Conference on Concurreny Theory, CONCUR 2005, held in San Francisco, CA, USA in August 2005. The 38 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 100 submissions. Among the topics covered are concurrency related aspects of models of computation, Petri nets, model checking, game semantics, process algebras, real-time systems, verification techniques, secrecy and authenticity, refinement, distributed programming, constraint logic programming, typing systems and algorithms, case studies, tools, and environment for programming and verification.

This book constitutes the refereed proceedings of the 5th International Symposium, Latin American Theoretical Informatics, LATIN 2002, held in Cancun, Mexico, in April 2002. The 44 revised full papers presented together with a tutorial and 7 abstracts of invited contributions were carefully reviewed and selected from a total of 104 submissions. The papers presented are devoted to a broad range of topics from theoretical computer science and mathematical foundations, with a certain focus on algorithmics and computations related to discrete structures.

Geometry and Topological Concepts is an exploration of the fundamental principles and applications of geometry and topology in mathematics and related fields. This book delves into the intricacies of shapes, sizes, and the properties of space, emphasizing the connections between these areas of study. It covers essential topics such as Euclidean and non-Euclidean geometries, topological spaces, and geometric transformations, providing readers with both theoretical foundations and practical examples. Ideal for students and professionals, it fosters a deeper understanding of the mathematical structures that underpin our world.

This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.

Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. - Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews - Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding - Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols - Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises

ETAPS2002wasthe?fthinstanceoftheEuropeanJointConferencesonTheory and Practice of Software. ETAPS is an annual federated conference that was established in 1998 by combining a number of existing and new conferences. This year it comprised 5 conferences (FOSSACS, FASE, ESOP, CC, TACAS), 13 satellite workshops (ACL2, AGT, CMCS, COCV, DCC, INT, LDTA, SC, SFEDL, SLAP, SPIN, TPTS, and VISS), 8 invited lectures (not including those speci?c to the satellite events), and several tutorials. The events that comprise ETAPS address various aspects of the system - velopmentprocess,includingspeci?cation,design,implementation,analysis,and improvement. The languages, methodologies, and tools which support these - tivities are all well within its scope. Di?erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on one hand and soundly-based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.