There are various kinds of computational problems. However in an introduction to computational complexity theory course it is easier to focus on decision problem, i.e. problems where the answer is either YES or NO. There are other kinds of computational problems but most of the time questions about them can be reduced to similar questions about ...

Arithmetic circuit complexity (or algebraic complexity theory) deals with the complexity of computing various polynomials. Important complexity classes here are VP and VNP, and geometric complexity theory is an important project attempting to separate VP and VNP (and later P and NP) using algebraic geometry and representation theory.

2019年6月28日 · Complexity theory is interested in a fine-grained classification of computable problems, with "it's uncomputable" as a worst-case scenario where we throw up our hands and give up. Computability theory (though one wouldn't realise this from an undergrad course) is interested in a fine-grained classification of uncomputable problems, with "it's ...

2016年8月2日 · I wonder if there exists any source of exercises\problems that are quite easier than those provided in Computational complexity: A modern approach so that I can train myself with the basic notions\constructions etc before tackling more complicated exercises. Also, a source of (quite-detailed) proofs of the main theorems would be great since ...

2019年6月18日 · I read that complexity theory is the study of complex systems. While I associate computational complexity theory with classification of problems.

2014年10月5日 · Basic discrete probability theory (linearity of expectation, Markov's and Chebyshev's inequalities, Bernoulli random variable, binomial distribution, indicator variables). Very helpful. Part of it (Chernoff's bound) you will learn as part of your study.

2020年6月18日 · The purpose of this book is to provide the basics, some history and a glimpse into the research in some areas of computational complexity theory, aimed at mathematics students. As such, this book is not a replacement for an introductory book such as Sisper's, but can be read independently to get a feeling what some sub-fields of complexity ...

2017年9月21日 · The structural complexity theory or simply structural complexity is the study of complexity classes, rather than computational complexity of individual problems and algorithms I did not get the last line "rather than computational complexity of individual problems and algorithms " I mean in complexity theory we focus on complexity classes not ...

2020年9月28日 · I will be taking a computational complexity theory course in about a year, and as the reference material will be Computational Complexity A Modern Approach I am more than confident that without a proper preparation that course will eat me alive. The book seems to have excellent practise problems in the sense that it will build up my CS toolbox.

Classic texts on computational complexity include Hopcroft & Ullman's text {1} and Sipser's text {2}. With patience, they should both be accessible. {1} Hopcroft, John E., R. Motwani, and J. D. Ullman.