¢ The Polynomial Technique; proving closure properties of PP (and related complexity classes) by constructing gap functions, a special kind of counting function which counts the difference between the number of accepting and rejecting computation paths of nondeterministic Turing machines. Opinion Both books discuss complexity theory, but base their approach on different goals and different underlying principles. Homer and Selman concentrate on a fairly straightforward introduction of computation and complexity which uses the standard approach of introducing Turing machines, and then using those to discuss the complexity of problems in P and in NP. I would have liked to see a few more examples, particularly of reductions, but in general this is a book that flows easily and quickly from topic to topic. Hemaspaandra and Ogihara take a diametrically opposed approach, choosing to concentrate on underlying techniques and algorithms rather than on introducing and dissecting specific complexity classes. It is assumed that the reader is already familiar with the various complexity classes, so that it is possible to concentrate on the various techniques. Each of the chapters is reasonably self-contained, although I found myself frequently going back to the appendix for definitions. As textbooks, the Homer-Selman book provides
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Mathematical theory of domains
Hestand, P. Daniel
Follow ACM SIGACT News
, Volume 33 (3)
Association for Computing Machinery – Sep 1, 2002
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