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Re:Ask HN: Good books on computational complexity? by gcv on Tuesday July 08, 2008 @06:26PM (#240450)
The best book on the subject I know of is Introduction to the Theory of Computation, by Michael Sipser. Very readable and lucid. Great exercises.
Re:Ask HN: Good books on computational complexity? by neilc on Tuesday July 08, 2008 @07:38PM (#240519)
Yes, definitely the best introductory book on the subject I've ever seen. Indeed, the Sipser book is a model for how to write a very readable, accessible CS theory textbook.

As far as how complexity theory on parallel computing, communication complexity is one related approach:

http://en.wikipedia.org/wiki/Communication_complexity

which provides a rigorous way to characterize how much communication is inherently required to solve a particular problem.