On the power of a threshold gate at the top

✍ Scribed by Mikael Goldmann

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 606 KB
• Volume: 63
• Category: Article
• ISSN: 0020-0190
• DOI: 10.1016/s0020-0190(97)00141-5

✦ Synopsis

The 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 H&tad's switching-lemma. @ 1997 Elsevier Science B.V.