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Electronic Colloquium on Computational Complexity

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Reports tagged with algebras:
TR08-099 | 19th November 2008
Gábor Ivanyos, Marek Karpinski, Lajos Rónyai, Nitin Saxena

Trading GRH for algebra: algorithms for factoring polynomials and related structures

In this paper we develop techniques that eliminate the need of the Generalized
Riemann Hypothesis (GRH) from various (almost all) known results about deterministic
polynomial factoring over finite fields. Our main result shows that given a
polynomial f(x) of degree n over a finite field k, we ... more >>>

TR13-011 | 10th January 2013
Nader Bshouty

Multilinear Complexity is Equivalent to Optimal Tester Size

In this paper we first show that Tester for an $F$-algebra $A$
and multilinear forms (see Testers and their Applications ECCC 2012) is equivalent to multilinear
algorithm for the product of elements in $A$
(see Algebraic
complexity theory. vol. 315, Springer-Verlag). Our
result is constructive in deterministic polynomial time. ... more >>>

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