Formal Models Of Computation The Ultimate Limits Of Computing

Formal Models Of Computation: The Ultimate Limits Of Computing

This book provides new presentations of standard computational models that help avoid pitfalls of the conventional description methods. It also includes novel approaches to some of the topics that students normally find the most challenging. The presentations have evolved in response to student feedback over many years of teaching and have been well received by students.The book covers the topics suggested in the ACM curriculum guidelines for the course on “Theory of Computation”, and in the course on “Foundations of Computing” in the model liberal arts curriculum. These are standard courses for upper level computer science majors and beginning graduate students.The material in this area of computing is intellectually deep, and students invariably find it challenging to master. This book blends the three key ingredients for successful mastery. The first is its focus on the mingling of intuition and rigor that is required to fully understand the area. This is accomplished not only in the discussion and in examples, but also especially in the proofs. Second, a number of practical applications are presented to illustrate the capacity of the theoretical techniques to contribute insights in a variety of areas; such presentations greatly increase the reader's motivation to grasp the theoretical material. The student's active participation is the third and final major element in the learning process, and to this end an extensive collection of problems of widely differing difficulty is incorporated.

Formal models of computation: the ultimatelimits of computing

Mathematics and Computation

From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography