# Reducing the complexity of reductions

@inproceedings{Agrawal1997ReducingTC,
title={Reducing the complexity of reductions},
author={Manindra Agrawal and E. Allender and R. Impagliazzo and Toniann Pitassi and S. Rudich},
booktitle={STOC '97},
year={1997}
}
We build on the recent progress regarding isomorphisms of complete sets that was reported in Agrawal et al. (1998). In that paper, it was shown that all sets that are complete under (non-uniform) AC0 reductions are isomorphic under isomorphisms computable and invertible via (non-uniform) depth-three AC0 circuits. One of the main tools in proving the isomorphism theorem in Agrawal et al. (1998) is a “Gap Theorem”, showing that all sets complete under AC0 reductions are in fact already complete… Expand
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