Lecture 5: Razborov-Smolensky Lower Bounds for Constant-Depth Circuit with MODp Gates
نویسنده
چکیده
In this lecture, we will talk about circuit lower bound for constant-depth circuit with MODp gates. Using switching lemma, we can prove exponential size lower bound for constant-depth circuit computing parity and majority. What if parity (=MOD2 gates) are allowed? It was conjectured that majority still needs exponential size to compute in constant-depth circuit. Razborov (1987) solves this conjecture, that is, majority requires exponential size to compute even if MOD2 gates are allowed. Smolenksy (1987) strengths this result, which says even MODq requires exponential size to compute when MODp gates are allowed, where p, q are different primes.
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