Complexity Theory Retrospective

In 1965 Juris Hartmanis and Richard E. Stearns published a paper "On the Computational Complexity of Algorithms". The field of complexity theory takes its name from this seminal paper and many of the major concepts and issues of complexity theory were introduced by Hartmanis in subsequent work. In honor of the contribution of Juris Hartmanis to the field of complexity theory, a special session of invited talks by Richard E. Stearns, Allan Borodin and Paul Young was held at the third annual meeting of the Structure in Complexity conference, and the first three chapters of this book are the final versions of these talks. They recall intellectual and professional trends in Hartmanis' contributions. All but one of the remainder of the chapters in this volume originated as a presentation at one of the recent meetings of the Structure in Complexity Theory Conference and appeared in preliminary form in the conference proceedings. In all, these expositions form an excellent description of much of contemporary complexity theory.

This volume provides a survey of the subject in the form of a collection of articles written by experts, that together provides a comprehensive guide to research. The editors'aim has been to provide an accessible description of the current stae of complexity theory, and to demonstrate the breadth of techniques and results that make this subject so exciting. Thus, papers run the gamut from sublogarithmic space to exponential time, and from new combinatorial techniques to interactive proof systems.

This volume provides a survey of the subject in the form of a collection of articles written by experts, that together provides a comprehensive guide to research. The editors'aim has been to provide an accessible description of the current stae of complexity theory, and to demonstrate the breadth of techniques and results that make this subject so exciting. Thus, papers run the gamut from sublogarithmic space to exponential time, and from new combinatorial techniques to interactive proof systems.

Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions and problems from cryptology. This book takes account of this situation, and therefore its subject is what may be dubbed "cryptocomplexity'', a kind of symbiosis of these two areas. This book is written for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation. Moreover, it may serve as a valuable source for researchers, teachers, and practitioners working in these fields. Starting from scratch, it works its way to the frontiers of current research in these fields and provides a detailed overview of their history and their current research topics and challenges.

This revised and extensively expanded edition of Computability and Complexity Theory comprises essential materials that are core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations. Subsequent chapters move from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability focus on the limitations of computability and the distinctions between feasible and intractable. Substantial new content in this edition includes: a chapter on nonuniformity studying Boolean circuits, advice classes and the important result of Karp─Lipton. a chapter studying properties of the fundamental probabilistic complexity classes a study of the alternating Turing machine and uniform circuit classes. an introduction of counting classes, proving the famous results of Valiant and Vazirani and of Toda a thorough treatment of the proof that IP is identical to PSPACE With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool. Topics and features: Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner Provides key mathematical background information, including sections on logic and number theory and algebra Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes

This book constitutes the refereed proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2009, held in Špindleruv Mlýn, Czech Republic, in January 2009. The 49 revised full papers, presented together with 9 invited contributions, were carefully reviewed and selected from 132 submissions. SOFSEM 2009 was organized around the following four tracks: Foundations of Computer Science; Theory and Practice of Software Services; Game Theoretic Aspects of E-commerce; and Techniques and Tools for Formal Verification.

Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics