Reducing the complexity of reductions

  title={Reducing the complexity of reductions},
  author={Manindra Agrawal and E. Allender and R. Impagliazzo and Toniann Pitassi and S. Rudich},
  booktitle={STOC '97},
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
Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem
Comparing reductions to NP-complete sets
Verifying proofs in constant depth
On the (Non) NP-Hardness of Computing Circuit Complexity
Strong Reductions and Isomorphism of Complete Sets
The Descriptive Complexity Approach to LOGCFL
Proofs, codes, and polynomial-time reducibilities
  • Ravi Kumar, D. Sivakumar
  • Computer Science, Mathematics
  • Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
  • 1999
Uniform constant-depth threshold circuits for division and iterated multiplication


On Uniformity within NC¹