By
Marius Zimand, Townson University, Townson, USA.
Description
There has been a common perception that computational complexity is a theory of "bad news" because its most typical results assert that
various real-world and innocent-looking tasks are infeasible. In fact, "bad news" is a relative term, and, indeed, in some situations
(e.g., in cryptography), we want an adversary to not be able to perform a certain task. However, a "bad news" result does not automatically
become useful in such a scenario. For this to happen, its hardness features have to be quantitatively evaluated and shown to manifest
extensively.
The book undertakes a quantitative analysis of some of the major results in complexity that regard either classes of
problems or individual concrete problems. The size of some important classes are studied using resource-bounded topological and measure-theoretical
tools. In the case of individual problems, the book studies relevant quantitative attributes such as approximation properties or the
number of hard inputs at each length.
One chapter is dedicated to abstract complexity theory, an older field which, however, deserves
attention because it lays out the foundations of complexity. The other chapters, on the other hand, focus on recent and important developments
in complexity. The book presents in a fairly detailed manner concepts that have been at the centre of the main research lines in complexity
in the last decade or so, such as: average-complexity, quantum computation, hardness amplification, resource-bounded measure, the relation
between one-way functions and pseudo-random generators, the relation between hard predicates and pseudo-random generators, extractors,
derandomization of bounded-error probabilistic algorithms, probabilistically checkable proofs, non-approximability of optimization problems,
and others.
The book should appeal to graduate computer science students, and to researchers who have an interest in computer science
theory and need a good understanding of computational complexity, e.g., researchers in algorithms, AI, logic, and other disciplines.
Included in series
North-Holland Mathematics Studies
Audience:
University libraries, researchers in the field theory of computation, computational complexity, algorithms, and al graduate students in computer science.
