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Summary: Morphisms of Rings and Applications to
Complexity
A Thesis Submitted
in Partial Fulfilment of the Requirements
for the Degree of
Doctor of Philosophy
by
Nitin Saxena
to the
DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KANPUR
June, 2006
CERTIFICATE
Certified that the work contained in the thesis entitled "Mor-
phisms of Rings and Applications to Complexity", by "Nitin
Saxena", has been carried out under my supervision and that
this work has not been submitted elsewhere for a degree.
(Dr. Manindra Agrawal)
Professor,
Department of Computer Science &
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