# Reducing the complexity of reductions

@article{Agrawal2001ReducingTC, title={Reducing the complexity of reductions}, author={Manindra Agrawal and Eric Allender and Russell Impagliazzo and Toniann Pitassi and Steven Rudich}, journal={computational complexity}, year={2001}, volume={10}, pages={117-138} }

Abstract. 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…

## 20 Citations

Comparing Reductions to NP-Complete Sets

- Computer ScienceICALP
- 2006

Under the assumption that NP does not have p-measure 0, reductions to NP-complete sets are investigated and it is proved that adaptive reductions are more powerful than nonadaptive reductions and every problem that is complete for NE is complete under one-to-one, length-increasing reductions that are computed by polynomial-size circuits.

Verifying proofs in constant depth

- Mathematics, Computer ScienceTOCT
- 2013

This paper investigates the question which languages admit proof systems in this very restricted model of proof systems where verification of proofs proceeds by NC0 circuits and shows that even easy regular languages such as Exact-OR do not admit NC0 proof systems.

Verifying proofs in constant depth

- Mathematics, Computer ScienceMFCS 2011
- 2011

This paper investigates the question which languages admit proof systems in this very restricted model of NC0, and shows that even easy regular languages such as Exact-OR do not admit NC0 proof systems.

On the (Non) NP-Hardness of Computing Circuit Complexity

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2014

It is shown that MCSP is provably not NP-hard under O(n1/2-e)-time projections, and it is proved that the Σ2P-hardness of NMCSP, even under arbitrary polynomial-time reductions, would imply EXP ⊄ P/poly.

A Functorial Approach to Reductions among Decision Problems

- Computer Science
- 2018

Characterizing complexity classes is not enough; structural complexity theorists are looking for lower bounds, and logical characterizations are good at giving us information about the structure of the programs corresponding to a certain complexity, but it is this latter information that is missing in the question of proving lower bounds.

The Complexity of Membership Problems for Circuits over Sets of Positive Numbers

- MathematicsFCT
- 2007

It is shown that the membership problem for the general case and for (∪∩,+,×) is PSPACE-complete, whereas it is NEXPTIME-hard if one allows 0, and several other cases are resolved.

Uniform constant-depth threshold circuits for division and iterated multiplication

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2002

Deterministic Search for CNF Satisfying Assignments in Almost Polynomial Time

- Computer Science, Mathematics2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

A deterministic algorithm is given which, given an n-variable CNF formula F that has at least ≥ 2^n satisfying assignments, runs in time and outputs a satisfying assignment of F.

Local Reductions

- Computer Science, MathematicsICALP
- 2013

For any time T ≥ n and parameter r ≤ n the authors obtain log2 |φ| = max(log T, n/r)+O (log n)+O(log log T ) and each output bit of C is a decision tree of log2.

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