# NEXP Does Not Have Non-uniform Quasipolynomial-Size ACC Circuits of o(loglogn) Depth

@article{Wang2011NEXPDN, title={NEXP Does Not Have Non-uniform Quasipolynomial-Size ACC Circuits of o(loglogn) Depth}, author={Fengming Wang}, journal={Electron. Colloquium Comput. Complex.}, year={2011}, volume={18}, pages={17} }

ACCm circuits are circuits consisting of unbounded fan-in AND, OR and MODm gates and unary NOT gates, where m is a fixed integer. We show that there exists a language in non-deterministic exponential time which can not be computed by any non-uniform family of ACCm circuits of quasipolynomial size and o(log log n) depth, where m is an arbitrarily chosen constant.

## 10 Citations

Nonuniform ACC Circuit Lower Bounds

- Computer ScienceJACM
- 2014

The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms entail these lower bounds, while the second step requires a strengthening of the author’s prior work.

A Satisfiability Algorithm for Depth Two Circuits with a Sub-Quadratic Number of Symmetric and Threshold Gates

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2016

A deterministic algorithm that, given a circuit with n variables andm gates, counts the number of satisfying assignments in time 2 n−Ω, which runs in time super-polynomially faster than 2 n if m= O(n2/ logbn) for some constant b> 0.

Non-uniform ACC Circuit Lower Bounds

- Computer Science2011 IEEE 26th Annual Conference on Computational Complexity
- 2011

The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds.

Depth-Reduction for Composites

- Computer Science2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
- 2016

A new depth-reduction construction is obtained, which implies a super-exponential improvement in the depth lower bound separating NEXP from non-uniform ACC, and it is shown that every circuit with AND, OR, NOT, and MODm gates can be reduced to a depth-2, SYM-AND circuit.

Circuits with composite moduli

- Computer Science
- 2016

The main result is that every ACC circuit of polynomial size and depth d can be reduced to a depth-2 circuit SYM◦AND of size 2(logn)O(d) , which improves exponentially the previously best-known construction by Yao-Beigel-Tarui, which has size blowup 2 2O( d) .

Circuit Complexity: New Techniques and Their Limitations

- Computer Science, Mathematics
- 2017

The weighted gate elimination method is introduced, which runs a more sophisticated induction than gate elimination, and it is shown that this method gives a much simpler proof of a stronger lower bound of 3.11n for quadratic dispersers.

Bounded depth circuits with weighted symmetric gates: Satisfiability, lower bounds and compression

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 2019

Bounded Depth Circuits with Weighted Symmetric Gates: Satisfiability, Lower Bounds and Compression

- Computer Science, MathematicsMFCS
- 2016

This paper presents algorithms for the circuit satisfiability problem of bounded depth circuits with AND, OR, NOT gates and a limited number of weighted symmetric gates that run in time super-polynomially faster than 2^n even when the number of gates is super- polynomial and the maximum weight of asymmetric gates is nearly exponential.

Circuit Size Lower Bounds and #SAT Upper Bounds Through a General Framework

- Computer Science, MathematicsMFCS
- 2016

This paper provides a general framework for proving worst/average case lower bounds for circuits and upper bounds for #SAT that is built on ideas of Chen and Kabanets, and shows that many known proofs (of circuit size lower bounds and higher bounds for#SAT) fall into this framework.

Gate elimination: Circuit size lower bounds and #SAT upper bounds

- Computer Science, MathematicsTheor. Comput. Sci.
- 2018

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