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, andrelative 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 classesa
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 Todaa 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 mannerProvides
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
"
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