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On Derandomizing Tests for Certain Polynomial Identities Manindra Agrawal

Summary: On Derandomizing Tests for Certain Polynomial Identities
Manindra Agrawal
Dept of CSE, IIT Kanpur 208016, India
email: manindra@iitk.ac.in
We extract a paradigm for derandomizing tests for poly-
nomial identities from the recent AKS primality testing al-
gorithm. We then discuss its possible application to other
1 Introduction
Polynomial identity testing has been in news recently
due to two major results proved last year: Kabanets and Im-
pagliazzo [3] proved that any derandomization of a random-
ized algorithm for the problem results in a lower bound on
arithmetic circuits, while Agrawal, Kayal, and Saxena [2]
gave a complete derandomization of the test for a specific
identity resulting in a deterministic polynomial-time algo-
rithm for primality testing. Viewed optimistically, these re-
sults suggest that lower bounds on arithmetic circuits might
be easier to obtain than we believe. In this paper, we try


Source: Agrawal, Manindra - Department of Computer Science and Engineering, Indian Institute of Technology Kanpur


Collections: Computer Technologies and Information Sciences