Summary: Com S 631: Lower bounds and Separation Results
Lecture 8 Scribe: David Lastine
In the last lecture we showed a n3/2
lower bound on the formula size of parity. We used
the following technical lemma.
Lemma 1. PraRk
2 FSize(f)] 3
Today we will exhibit an explicit function whose formula complexity is ~O(n5/2
). For this
result we need a notion of sub function. Let f : n
and g : m
, m n be two
functions. We say that g is a sub function of f if there is exists a Rm such that g = f|a.
We use the following observation.
Observation 1. If g is a sub function of f, then FSize(g) FSize(f).