Weizmann Logo
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style

Reports tagged with parity gate:
TR12-071 | 29th May 2012
Kazuhisa Seto, Suguru Tamaki

A Satisfiability Algorithm and Average-Case Hardness for Formulas over the Full Binary Basis

We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis.
For formulas of size at most $cn$, our algorithm runs in time $2^{(1-\mu_c)n}$ for some constant $\mu_c>0$.
As a byproduct of the running time analysis of our algorithm,
we get strong ... more >>>

TR19-073 | 17th May 2019
Igor Carboni Oliveira, Rahul Santhanam, Srikanth Srinivasan

Parity helps to compute Majority

We study the complexity of computing symmetric and threshold functions by constant-depth circuits with Parity gates, also known as AC$^0[\oplus]$ circuits. Razborov (1987) and Smolensky (1987, 1993) showed that Majority requires depth-$d$ AC$^0[\oplus]$ circuits of size $2^{\Omega(n^{1/2(d-1)})}$. By using a divide-and-conquer approach, it is easy to show that Majority can ... more >>>

ISSN 1433-8092 | Imprint