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Results tagged with complexity-theory
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user 152398
Questions related to the (computational) complexity of solving problems
5
votes
Accepted
Are there superexponential NP-complete problems?
I’m not sure how you define “superexponential”, could you make it precise for me?
If you define "super-exponential" as something described in the previous link like $2^{n^c}$:
In this context, $O(n!)$ …
- 311
1
vote
1
answer
49
views
construct language in ${\sf BPP \backslash (RP \cup coRP)}$ assuming $\sf RP \neq ZPP$
Problem
This is a HW problem from CMU 15-455 (hw10, p1(a)), spring 17 by Ryan O'Donnell.
Assume $L \in {\sf RP \backslash ZPP}$. Define
$$ L' = \left\{ (x, y) : \text{either $x \in L$ and $y \notin L$ …
- 311
2
votes
Probabilistic methods for undecidable problem
What do you mean by randomness on nondeterministic TM? I think such a NTM with correct probability $\geq 2/3$ should be in PH by Sipser-Lautemann, and with probability 50% it's like something related …
- 311
2
votes
Reduce Subset-Sum to Sat
I think a direct reduction can be done by the following process:
setup a enable gate $e_i$ for each integer $x_i$ (then we can represent each bit of $x_i$ using $e_i$ and $0$), add all integers (with …
- 311
3
votes
0
answers
41
views
Can fine-grained hardness be proved directly from classical hardness (e.g., $\sf P \neq NP$)...
I have just learnt about some typical result of fine-grained hardness in 15-455 by Prof Ryan: CNF-SETH implies ${\sf DIAMETER} \notin {\sf TIME}(mn^{1-\epsilon})$. (Here DIAMETER stands for the graph …
- 311
1
vote
How can we show that P is not closed under taking all long prefixes?
In fact Yuval's hint is all the solution you need: consider instance $I$ of any $\mathsf{NP}$-complete problem (e.g. 3SAT) and its proof $c$, let the proof appear in the second half of the constructed …
- 311