Questions tagged [nc]
8 questions
6
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1 answer
What is the relation between NC and P/poly?
I am unable to see a clear explanation of how the classes NC and P/poly intersect or not. (and if they do intersect then how and where? and if not then what is the proof?)
user6818
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2
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1 answer
Are classes $\textbf{NC}$ and uniform $\textbf{NC}$ the same?
On page 117 in Arora and Barak, the definition of class $\textbf{NC}$:
For every $d$, a language $L$ is in $\textbf{NC}^d$ if $L$ can be decided
by a family of circuits $\{C_n\}$ where $C_n$ has poly(n) size and depth $O(\log^d n)$. The class…
minh quý lê
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1
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1 answer
Confusing on the proof $\textbf{NC}^1\subseteq \textbf{L}$ using DFS
On page 430 of Sisper's TOC, Theorem 10.39 proves $\textbf{NC}^1\subseteq \textbf{L}$:
PROOF: We sketch a log space algorithm to decide a language $A$ in $\textbf{NC}^1$ . On
input $w$ of length $n$, the algorithm can construct the description as…
minh quý lê
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1
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2 answers
Symmetric functions in NC¹
A boolean function $f \colon \{0,1\}^n \rightarrow \{0,1\}$ is symmetric if $f(x)$ depends only on the number of $1$s in $x$.
It is known that every boolean function is in $\mathrm{NC}^1$, i.e. there is a circuit of depth $O(\log n)$ computing…
Larry a.
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1
vote
2 answers
Why sum of two binary numbers cannot be determined in $NC^0$ but in $AC^0$?
Why sum of two binary numbers cannot be determined in $NC^0$ but it can be determined in $AC^0$?
samTT
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0
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Given a PRAM may use arbitrarily many processors, why is Hamiltonian Cycle not in NC?
In my parallel algorithms class, the PRAM model is described as having an "arbitrary number of processors, bounded by some polynomial in the input size."
I think that this may be missing a constraint. For example, this would imply that finding a…
Real John Connor
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Prove that $\textbf{NC}$ circuit family can compute log space reduction
Most proofs of the problem that I have seen stop at proving $\textbf{NL}\subseteq \textbf{NC}^2$ and not explicitly point out the circuit. I'm trying to show that $\textbf{NC}$ circuit family can compute log space reduction by constructing…
minh quý lê
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Is checking GCD in NC or strongly P?
Given two integers $m$ and $n$ computing $\mathsf{GCD}(m,n)$ is not known to be either in $NC$ or in strongly Polynomial time.
Given three integers $m$, $n$ and $g$, is testing $g=\mathsf{GCD}(m,n)$ or not in either $NC$ or in strongly Polynomial…
Turbo
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