today
	barrier results
	natural proofs
relativization
	relativize
	circuit complexity relativizes?
		oracle gates
		thm: any oracle A, P^A\subseteq SIZE^A(\poly) 
		but: 
			PARITY\notin AC^0 not clear how to relativize
		but:
			lack of relativizing proofs does not rule out the result relativizing
	Q. barrier results for circuit complexity?
				communication complexity?
	Q. "known techniques" = ?
communication complexity
	recall
	prop: EQ requires \ge n bits of communication
	Pf(from before): fooling set
	prop: f(x,y) requires D(f)\ge \log\rank_\F_\R(M_f), any field \F
	pf
		partition M_f into rectangles
	prop: EQ requires \ge n bits of communication
	pf:
		\rank M_{EQ}=2^n for any field \F
	rmk:
		rank lower bound is natural proof for CC lb
			constructivity
				via determinant
			largeness
				via counting low rank decompositions over F_2
	motivations
		largeness
			random functions are hard
		constructivity
			most mathematical reasoning is effective
	fooling set method is not
		constructive
		large
natural proofs
	general definition of a natural property
		draw picture
			v. few
		useful
		polytime efficient
		accepts 1/poly fraction of elements
	natural ckt lbs
		usefulness
		constructivity
		largeness
	non-examples
		P(f)=0 if f is simple
			large
			not constructive
		P(f)=1 if f is SAT
			not large
			is constructive
	examples
		AC^0 lb via random restrictions
			set n-n^\eps input bits
			is constructive
			is also large
		AC^0[2] lb for parity
			more challenging, but can do it
	def:
		OWF
		PRG
		PRF
	thm[GGM]: PRG=>PRF
	pf
		sketch
	thm[RazborovRudich] weakly-exponentially secure PRFs
			=> no natural proofs against SIZE(n^c) for some c
	pf
perspective
	conjectured PRFs "just beyond" AC^0
	relaxing largeness
		via problem structure
			ie, downward self-reductions
		via completeness
			contradict time-heirarchy theorem
				used in william's AC^0[m] lb for NEXP
	relaxing constructivity
		diagonalization
		???