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The Isomorphism Conjecture for Constant Depth Manindra Agrawal

Summary: The Isomorphism Conjecture for Constant Depth
Manindra Agrawal
IIT Kanpur
March 6, 2010
For any class C closed under TC0
reductions, and for any measure
u of uniformity containing Dlogtime, it is shown that all sets complete
for C under u-uniform AC0
reductions are isomorphic under u-uniform
-computable isomorphisms.
1 Introduction
One of the long-standing conjectures about the structure of complete sets is the
isomorphism conjecture (proposed in [BH77]) stating that all sets complete for
NP under polynomial-time reductions are polynomial time isomorphic. As the
conjecture cannot be resolved either way unless we discover non-relativizable
techniques (see [KMR88, KMR95, FFK96] for more details), efforts have been
made to prove the conjecture in restricted settings by restricting the power of


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


Collections: Computer Technologies and Information Sciences