Representing (0, 1)-matrices by boolean circuits

@article{Jukna2010Representing1,
  title={Representing (0, 1)-matrices by boolean circuits},
  author={Stasys Jukna},
  journal={Discrete Mathematics},
  year={2010},
  volume={310},
  pages={184-187}
}
A boolean circuit represents an n by n(0, 1)-matrix A if it correctly computes the linear transformation E y = AEx over GF(2) on all n unit vectors. If we only allow linear boolean functions as gates, then somematrices cannot be represented using fewer thanΩ(n2/ ln n) wires. We first show that using non-linear gates one can save a lot of wires: anymatrix can be represented by a depth-2 circuit withO(n ln n)wires usingmultilinear polynomials over GF(2) of relatively small degree as gates. We… CONTINUE READING