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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
26
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Are there any interesting examples of random NP-complete problems?
Here's an example of the kind of thing I mean. Let's consider a random instance of 3-SAT, where you choose enough clauses for the formula to be almost certainly unsatisfiable, but not too many more th …
15
votes
3
answers
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Is this strange problem NP-complete?
The following quadratic expression can be simplified:
(x+1)(x+2) + (x+1)(x-3) + 2x(2x-1) - (3x+1)(x-3) - 2x(x+2).
What is the easiest way of doing the simplification? (It would be good to think abou …
29
votes
2
answers
1k
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A combination of two well-known complexity problems
Suppose you are given two graphs $G$ and $H$ and are told that one of the following two situations occurs. Either they are isomorphic, or one of the graphs contains a Hamilton cycle and the other does …
23
votes
2
answers
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What is the complexity of this problem?
Recently on Dick Lipton and Ken Regan's blog there was a post about problems of intermediate complexity, that is, NP problems that are harder than P but easier than NP-complete. The main message of th …
12
votes
1
answer
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Are there very strongly pseudorandom permutations?
A pseudorandom permutation can be defined formally as a function $\phi$ from $\{0,1\}^k\times\{0,1\}^n$ to $\{0,1\}^n$ such that for every $x\in\{0,1\}^k$ the function $\phi_x:y\mapsto\phi(x,y)$ is a …