On the power of a threshold gate at the top
1997; Elsevier BV; Volume: 63; Issue: 6 Linguagem: Inglês
10.1016/s0020-0190(97)00141-5
ISSN1872-6119
Autores Tópico(s)Quantum Computing Algorithms and Architecture
ResumoThe discriminator lemma is normally used to prove lower bounds for circuits with small-weight threshold gates. In this note we adapt the lemma to circuits with a general (large-weight) threshold gate at the top. The new lemma is used to give a new proof of a previously known lower bound for the size of a threshold of parity gates that computes inner product mod 2, and to prove that a small-depth AND-OR circuit for parity must have exponential size even if we allow a threshold gate at the top. The latter result is a generalization to large weights of a result by Green, and depends heavily on Håstad's switching-lemma.
Referência(s)