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It's a homework assignment, we were asked to read, understand, and present to our colleagues a short paper/article (suggested 4-6 pages) for our Computability, Decidability or Complexity class.

The articles I was able to find in the past couple days using google scholar a way over what we were taught, plus, 50-100+ pages is way over the scope of my assignment. In class, we were provided with an introduction to the three topics, complexity classes, relations between them, and (mostly informal) proofs for the most representative problems from each class by modelling them using all kinds of Turing Machines.

Any possible solutions? It's the first time in my life I'm touching anything related to research, I can barely understand even the scope of most papers I find.. I guess any advice would be welcome.

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5 Answers 5

up vote 7 down vote accepted

"By definition" recent research papers usually contain non-trivial results and they often (always?) require a deep knowledge of the argument in order to be well understood, so if you pick a paper at random you'll probably find a bunch of obscure signs in your hands :-)

So my suggestion is to look at "old" research papers (but not "too old"):

  1. pick a particular argument/theorem that you think you have understood informally (or an argument that intrigues you);
  2. read more about it on a theory of computation book or on Internet (for example start from Wikipedia and look at the references at the bottom, or search it on Google adding the keywords "introduction" or "lecture notes");
  3. finally search the paper in which that argument/theorem was originally published and read it;

For example one of the fundamental basic results in computational complexity is the (deterministic) Time Hierarchy theorem. Very informally the theorem says that given more time, a Turing machine can solve more problems. You can start reading the Wikipedia article, then pick a lecture note with a more formal proof Googling around (for example pick this one by Arora). Finally when you think that you've understood the proof well download and read the original paper R. Stearns and J. "Hartmanis paper On the computational complexity of algorithms", 1965. You'll find that it contains even more details and is more formal.

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Assuming "older" papers are ok, what about Stephen Cook's well known The Complexity of Theorem-Proving Procedures [1]? It is 8 pages long, and if for the most part you have been able to keep up in your computability class, you can likely keep up with this paper as well. A copy is freely available from the author's website, or alternatively you can get a "nicer" re-typed version here.

[1] Stephen A. Cook. 1971. The complexity of theorem-proving procedures. In Proceedings of the third annual ACM symposium on Theory of computing (STOC '71). ACM, New York, NY, USA, 151-158.

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I'd look at the "further reading" suggestions in your textbook. If the author made some effort here, the papers listed should be on-topic, important, and probably accessible.

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Alan Turing's paper On computable numbers, with an application to the Entscheidungsproblem, 1936 is an extremely important paper (it started the entire field, one could say), and it's also a pleasant read. Highly recommended reading.

Claude Shannon's paper A mathematical theory of Communication, 1948 is beautiful, though it might fall outside of the category of complexity theory, it is the paper that initiated information theory and might therefor be relevant.

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that's a paper with fundamental results to computer science, and communication engineering, but how does it relate to the author question ? –  AJed Jan 30 '13 at 4:17
    
@AJed I added Turing's On computable numbers, which should be related to computation. (Happy? :) ) –  Pål GD Jan 30 '13 at 15:18
    
whatever man (there is no need to use statemenst such as (happy ?) or any similar ones. I am not playing games here. I just asked you, how it is related ? [If you had a good answer, and apparently you don't, then I would have learnt something new in a field that I am not very much into]. –  AJed Jan 30 '13 at 15:38

This is an interesting history article titled "A Short History of Computational Complexity" which will give you a big picture in this area.

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