All reports by Author Piyush Kurur:

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TR08-023
| 10th January 2008
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Anindya De, Piyush Kurur, Chandan Saha, Ramprasad Saptharishi#### Fast Integer Multiplication using Modular Arithmetic

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TR04-121
| 7th December 2004
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Vikraman Arvind, Piyush Kurur, T.C. Vijayaraghavan#### Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy.

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TR03-064
| 23rd June 2003
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Vikraman Arvind, Piyush Kurur#### Upper Bounds on the Complexity of some Galois Theory Problems

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TR02-037
| 21st May 2002
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Vikraman Arvind, Piyush Kurur#### Graph Isomorphism is in SPP

Anindya De, Piyush Kurur, Chandan Saha, Ramprasad Saptharishi

We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for

multiplying two $N$-bit integers that improves the $O(N\cdot \log

N\cdot \log\log N)$ algorithm by

Sch\"{o}nhage-Strassen. Both these algorithms use modular

arithmetic. Recently, F\"{u}rer gave an $O(N\cdot \log

N\cdot 2^{O(\log^*N)})$ algorithm which however uses arithmetic over

complex numbers as opposed to ...
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Vikraman Arvind, Piyush Kurur, T.C. Vijayaraghavan

In this paper we study the complexity of Bounded Color

Multiplicity Graph Isomorphism (BCGI): the input is a pair of

vertex-colored graphs such that the number of vertices of a given

color in an input graph is bounded by $b$. We show that BCGI is in the

#L hierarchy ...
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Vikraman Arvind, Piyush Kurur

Given a polynomial f(X) with rational coefficients as input

we study the problem of (a) finding the order of the Galois group of

f(X), and (b) determining the Galois group of f(X) by finding a small

generator set. Assuming the generalized Riemann hypothesis, we prove

the following complexity bounds:

1. ... more >>>

Vikraman Arvind, Piyush Kurur

We show that Graph Isomorphism is in the complexity class

SPP, and hence it is in $\ParityP$ (in fact, it is in $\ModkP$ for

each $k\geq 2$). We derive this result as a corollary of a more

general result: we show that a {\em generic problem} $\FINDGROUP$ has

an $\FP^{\SPP}$ ...
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