today
	cook-levin
	alternation
cook levin
	Thm[Cook-Levin]
		NP\le CKT-SAT
	Prop: CKT-SAT\le 3-SAT
	Rmk: completes PSPACE\le TQBF
alternation
	ex
		=k clique
		P=NP => find satisfying assignment
		circuit minimization
	Q. how to formalize
	def: alternating TM
		states
		acceptance criteria
		ATIME
	def: AP
	prop: SPACE(s(n))\subseteq ATIME(s^2)\subseteq SPACE(s^2)
	cor: AP=PSPACE
	P \le NP,coNP\le AP=PSPACE
	Q. alternation as a resource?
	def: \Sigma^k-TIME, \Pi^k-TIME
		\Sigma^kP, \Pi^kP
		PH
	prop: =k clique in \Sigma^2 P and \Pi^2P
		circuit minimization in \Pi^2 P