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Results tagged with computational-complexity
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user 10035
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.
3
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$n!$ computation in $\mathsf{BSS}$ model
It is well known that if $n!$ cannot be computed in $\mathsf{polylog}(n)$ ring ($\Bbb Z$) operations, then $\mathsf P\neq\mathsf{NP}$ in $\mathsf{BSS}$ model.
Suppose if we assume $\mathsf P=\mathsf{ …
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7
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2
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2k
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Strassen's algorithm
I am reading Landsberg's "Tensors: Geometry and Applications". Here he mentions tensor formulation of Strassen's algorithm and shows that the rank of Strassen's matrix multiplication tensor is $7$ and …
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7
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Is integer GCD in NC?
Wikipedia, in the page http://en.wikipedia.org/wiki/Greatest_common_divisor#Complexity mentions integer GCD is in NC by citing http://www.cs.cornell.edu/courses/CS6820/2012sp/Handouts/Sedjelmaci07.pdf …
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1
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2
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672
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Finding minimum weight codeword of MDS RS code
For a $[n,k,n-k+1]_q$ Reed Solomon code is there a polynomial time algorithm to find at least one minimum weight $(n-k+1)$ codeword? I searched in literature and I could not find one and hence I am su …
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3
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1
answer
162
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Quick tests for Self complementary vertex transitive graphs
Are there any quick tests to determine if a graph is Self complementary vertex transitive? That is if the graph is self complementary vertex transitive the answer should be yes.
- 13.9k
2
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66
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$3$SAT generation with prescribed number of solutions
Given $n,k\in\Bbb N$ with $0\leq k \leq 2^n$ can we generate an uniformly random instance among all possible solutions of an $n$ variable $3$-SAT instance and exactly $k$ solutions in $poly(n\log k)$ …
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1
vote
2
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On complexity of a combinatorial number theoretic problem?
Given the matrix
$\begin{bmatrix}
r_{11}&\dots&r_{1n}\\
\vdots&\ddots&\vdots\\
r_{m1}&\dots&r_{mn}
\end{bmatrix}\in\Bbb Z^{m\times n}$ with $0<r_{ij}<2^n$ and $a,q\in\Bbb Z$ with $|a|,|q|<2^n$ what i …
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7
votes
1
answer
535
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Vertex transitive graphs
Does having vertex transitivity make the problem of calculating independence and chromatic numbers easier?
- 13.9k
1
vote
0
answers
143
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On variant of integer factorization
In the post on site cstheory.stackexchange on whether a variant of integer factorization
$$\mathsf{}\mbox{ }{\Pi} = \{\langle a, b, n \rangle \;|\; \exists \mbox{ } \mathsf{ an}\mbox{ }\mathsf{ intege …
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2
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Bit complexity versus arithmetic complexity of polynomial multiplication
Given degree $d_1$ and $d_2$ polynomials in $\Bbb Z[x]$ with coefficient sizes of bits $b_1$ and $b_2$ respectively
(1) what is the bit complexity of multiplying the two polynomials?
(2) What is th …
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0
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1
answer
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Turing and Many one reductions in computability versus complexity
What are some non-trivial (please exclude poly time definitional difference) differences between Turing versus Many-one reductions in computability theory and those that occur in complexity theory?
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1
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$\mathsf{NP}$ complete version of Skolem arithmetic
Definable subsets of $\mathbb N$ in the language of Presburger arithmetic are exactly the eventually periodic sets and quantifier free part corresponds to Integer Programming with linear inequalities. …
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0
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62
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On complexity of a particular prime problem
Is the following problem in $PH$ and is it complete for any class?
Problem: Is the $i$th bit of the $m$th prime $1$?
It appears to require a counting quantifier which has to demonstrate witness is the …
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3
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3
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A conjecture on a Subset Power Sum Problem motivated by Computer Science
Let $X=\{x_{1}, \cdots , x_{n}\}$ be a set of $n$ positive integers and integer $i \ge 1$. Let’s say that the set $X$ is $i$-sum-avoiding if for any nonnegative integers $c_{1}, \cdots, c_{n}$ such th …
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Complexity of $\mathsf{gcd}(a,b)\bmod N$
Given $a,b\in\Bbb N$ where each $a,b$ is $n$-bits, we can compute $\mathsf{gcd}(a,b)$ in $cn^{1+\epsilon}$ bit operations for some fixed $c\geq1$.
My query is given $N,a,b$ where $a,b$ is $n$-bits an …
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