Lecture 01 (09/26)

	Introduction; Turing machines; Decision problems; Complexity classes;
	L, NL, P, NP, PSPACE, EXP, etc.
	Basic hierarchy theorems

Lecture 02 (10/01)

	Reductions, completeness;
	Boolean circuits & generic completeness: CVP, Circuit-SAT, SAT, Oracle-SAT
		(Cor: NP subset of PSPACE)
	Other examples of NP completeness

Lecture 03 (10/03)

	NP-completeness, contd.
	Fagin's theorem (statement only) and the importance of NP
	Very hard optimization problems; Polynomial-time hierarchy

Lecture 04 (10/08)

	Reducibility and Completeness for space-bounded classes:
		1-GAP, GAP, Succinct-GAP, QBF
			(Cor: NL subset of P, PSPACE subset of EXP)
	
Lecture 05 (10/10)

	Savitch's theorem: NL subset of DSPACE[log^2 n]
			(Cor: NPSPACE = PSPACE)
	The Immerman--Szelepscenyi theorem: NL = coNL

	Time permitting:
	Counting problems; the classes #P and #L; #SAT and #STCON
	Completeness of the Permanent and the Determinant, resp., for these classes

Lecture 06 (10/15)

	The Boolean circuit model; parallel computation
	P/poly, AC^0, NC^1, NC^2, NC, SC
	Their relationship to L and NL:
		NC^1 subset of L subset of NL subset of NC^2
	Mention linear algebra

Lecture 07 (10/17)

	Brief discussion of "abstract" vs. "concrete" complexity results
		Parity not in AC^0; Hastad's switching lemma
		The results of Kannan, Nepomnjascii, Fortnow, Fortnow--van Melkebeek
			(eg., SAT not in DTISP[n polylog n, n^{0.99}]
	State both, prove one set.

Lecture 08 (10/22)

	Enter randomization: mention primality (yes!), zero-testing,
		perfect matching, Frievalds, USTCON.
	The classes RP, BPP, ZPP;
	BPP subset of PH (Sipser's proof); Valiant--Vazirani;

Lecture 09 (10/24)

	(Revisit) Counting complexity classes; the classes #P and PP
	Toda's theorem

Lecture 10 (10/29)

	USTCON - mention theorem of AKLLR; Nisan's pseudorandom generator
	RL subset of SC

Lecture 11 (10/31)

	Saks--Zhou: BPL subset of DSPACE[log^{3/2} n]

Lecture 12 (11/05)

	Efficient proof-checking via randomness:
		relaxations and restrictions (MA, PCP)
	MA subset of PH (co-NP subset of MA implies PH collapses)
	PCP and hardness of approximation (of clique)

Lecture 13 (11/07)

	NP subset of PCP[poly, 1]

Lecture 14 (11/12)

	NP subset of PCP[polylog, polylog]

Lecture 15 (11/14)

	NP subset of PCP[log, polylog]

Lecture 16 (11/19)
	Likely: No class due to FOCS
	Unlikely: Composition of PCPs, complete NP = PCP[log n, 1] and
		do a sketch of the low-degree tester in Lecture 17

Lecture 17 (11/21)

	Composition of PCPs, complete NP = PCP[log n, 1]

Lecture 18 (11/26)

	Interaction in proof-checking: AM, IP, Graph non-isomorphism
	AM = IP; AM[c] = AM[2]

Lecture 19 (12/03)

	IP = PSPACE;
	Multi-prover protocols, Proof systems; MIP = NEXPTIME

Lecture 20 (12/05)

	SZK; Graph isomorphism; SZK = IP with 1 bit (+ ugly restriction)