Complexity Theory: A Modern Approach
by Sanjeev Arora, Boaz Barak
Publisher: Cambridge University Press 2008
Number of pages: 489
This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to be a text and as well as a reference for self-study. This means it must simultaneously cater to many audiences, and it is carefully designed with that goal. The book will explain the context in which a certain notion is useful, and why things are defined in a certain way. Examples and solved exercises accompany key definitions. This book assumes essentially no computational background (though a slight exposure to computing may help) and very little mathematical background apart from the ability to understand proofs and some elementary probability on finite sample spaces. A typical undergraduate course on "Discrete Math" taught in many math and CS departments should suffice (together with the Appendix).
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by Luca Trevisan
Notes from a graduate courses on Computational Complexity. The first 15 lectures cover fundamentals, the remaining is advanced material: Hastad's optimal inapproximability results, lower bounds for parity in bounded depth-circuits, and more.
by R. G. Downey, D. R. Hirschfeldt - Springer
Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of algorithmic randomness and complexity for scientists from diverse fields.
by Johan Håstad
This set of notes gives the broad picture of modern complexity theory, defines the basic complexity classes, gives some examples of each complexity class and proves the most standard relations. The author emphasizes the ideas involved in the proofs.
by Ben Goertzel - Plenum Press
This text applies the concepts of complexity science to provide an explanation of all aspects of human creativity. The book describes the model that integrates ideas from computer science, mathematics, neurobiology, philosophy, and psychology.