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	bugfix in ps1
	I'm away next week:
		Robert:
			lecturing
			additional office hours: T2, R1, F2-4
today
	NP
	NP completeness
what is computing
	search
	verification
ex: factoring, primality
why NP
defn of NP as verification
defn of NTMs, NTIME(t(n))
prop: TIME(t(n))\subseteq NTIME(t(n))
prop: NTIME(t(n))\subseteq TIME(2^{O(t(n))})
Prop: P\subseteq MP\subseteq EXP=TIME(2^{poly(n)})
Prop: NP=NTIME(poly(n))
Q P vs NP
defn: NEXP
Q. NP=NEXP
Thm[NTIME heirarchy]:
	failed sketch
defn of coNP
Q. NP vs coNP?

defn of Karp reduction
	[[draw picture]]
properties
	A\le B, B\in P => A\in P
		[[polynomials compose]]
	A\le B, B\in NP => A\in NP
	complements
defn of NP-hard, NP-complete
Prop: L NP-complete. P=NP iff L\in P
Prop: L NP-complete. coNP=NP iff L\in NP
Prop: bounded-acceptance is NP-complete
thm[CookLevin]
thm: many natural NP-complete problems
	via reductions from 3SAT
	see hw
draw picture