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Questions related to the (computational) complexity of solving problems

19
votes
4answers
One possible motivation for studying computational complexity classes is to understand the power of different kinds of computational resources (randomness, non-determinism, quantum effects, etc.). If …
asked Aug 22 '13 by D.W.
10
votes
1answer
For reasoning about things like NP-completeness, we typically use many-one reductions (i.e., Karp reductions). This leads to pictures like this: (under standard conjectures). I'm sure we're all f …
asked Jun 14 '14 by D.W.
0
votes
2answers
2QBF is the following problem: given a CNF formula $\psi$ on $2n$ variables, determine the truth value of $$\forall x \in \{0,1\}^n . \exists y \in \{0,1\}^n . \psi(x,y).$$ Question: Is 2QBF in $P^{ …
asked Feb 22 '17 by D.W.
3
votes
0answers
Is there a simple example of a Boolean function $f:\{0,1\}^m \to \{0,1\}$ that we know can be computed by a polynomial-size circuit, but cannot be computed by any polynomial-size monotone circuit? Id …
asked Apr 20 '18 by D.W.
9
votes
4answers
Consider the following problem: Input: lists $X,Y$ of integers Goal: determine whether there exists an integer $x$ that is in both lists. Suppose both lists $X,Y$ are of size $n$. Is there a deter …
asked Feb 4 '15 by D.W.
18
votes
1answer
Thanks to the max-flow min-cut theorem, we know that we can use any algorithm to compute a maximum flow in a network graph to compute a $(s,t)$-min-cut. Therefore, the complexity of computing a minim …
asked Jun 9 '15 by D.W.
10
votes
2answers
What is the complexity of MIN-2-XOR-SAT and MAX_2-XOR-SAT? Are they in P? Are they NP-hard? To formalize this more precisely, let $$\Phi\left(\mathbf x\right)={\huge\wedge}_{i}^{n}C_i,$$ where $\ …
asked Nov 4 '13 by D.W.
24
votes
3answers
I'm interested in the question of how best to teach NP-completeness to computer science majors. In particular, should we teach it using Karp reductions or using Turing reductions? I feel that the co …
asked Oct 23 '13 by D.W.