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.
-Emphasis is on relevant quantitative attributes of important
results in complexity.
-Coverage is self-contained and accessible to a wide
audience.
-Large range of important topics including: derandomization
techniques, non-approximability of optimization problems,
average-case complexity, quantum computation, one-way functions and
pseudo-random generators, resource-bounded measure and topology.
General
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