Here are guidelines for the final project.
Assigment: You will find an example of a hardness result (NP-completeness, PSPACE-completeness, etc) in your area of interest and write a short summary/survey.
Problem selection: It doesn't have to be a foundational result in your field (e.g., "machine learning is hard because finding the smallest circuit matching a set of observations is NP-hard or whatever"). It's fine if it's a problem that appears in just one paper. I have only one paper with an NP-hardness result: it is just an optimization problem that arises naturally from trying to choose the best parameters for some very specific algorithm we developed. So it is fine if the hard problem is very narrow. The hardness reduction should also not be too trivial (e.g., "training a neural network is hard because a neural network can emulate any boolean circuit").
Length: Probably 3-6 pages. Any less than that, and the reduction is probably much too elementary.
Here are the criteria that I will be looking for:
Motivation of the result: Most likely there is an optimization problem or decision problem that would have been nice to solve quickly. But it turned out to be a hard problem. WHY would it have been nice to solve this problem -- i.e., what relevance does it have to a specific research question in your area? I'm probably not an expert in your field, so this will have be written for a more general audience (good practice!). I don't want you to teach me all of your field, and I don't want you to just say "someone came up with this problem in a paper" without any further details. Give the reader a sense of how the hard problem arises in the context of this research area.
Clearly state and describe the result: Define the problem and state what you are going to show about it. Then describe the proof of hardness. I want to see you describe a reduction. If you are doing a reduction from problem X, then it is fine to just state "X was previously known to be NP-hard/whatever [citation]". Fully argue the correctness of the reduction. If the reduction involves complicated "gadgets", try to show them and list the properties they have, but sometimes this is done just by exhaustive search. You don't have to do an exhaustive search but definitely list the properties needed by the gadgets and maybe give a few examples (think about the minesweeper NP-completeness gadgets).
Aftermath: Given that a hard problem has been identified, what happens next? Give up hope on this problem? Use heuristics? approximations? Identify special cases that can be solved more efficiently? Change the rules of the game?
Professional writing: Write something polished and beautiful that you'd be proud to put on your website as an example of your scholarly writing. Cite the relevant work. Unless you are proving a new hardness result with this project, give full credit to whoever did it first.
Deadline: June 12 (Monday of finals week)