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 ...

Oct 5, 2014 · 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.

Aug 2, 2016 · For example, there are about 10 lectures by Timoth Gowers on the web on complexity and quantum computation, I think they will be useful although his goal in complexity theory seems to be more towards lower bounds of circuits not introducing the topic for a novice but I think I can understand those lectures regarding complexity since I've ...

Sep 28, 2020 · 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.

The complexity of probability distributions comes up particularly in the study of distributional problems like DistNP in Levin's theory of average case complexity theory. A distribution is P-computable if its cumulative density function can be evaluated in polynomial time. A distribution is P-samplable if we can sample from them in polynomial time.

Mar 29, 2019 · The part you cite is from chapter 0 (i.e., not really a chapter), whereas the material for complexity theory only appears at the end (i.e., part three). This is why the passage is so fuzzy. Most likely it is intended only as motivation and to give a broad overview for the topics to be covered in the book.

Sep 21, 2017 · 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 ...

Jun 28, 2019 · 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 ...

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.

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.