ECS 220 - Winter 2006 - List of Lecture Topics

Wk Lect Topic

0 1 - R 1/5 Introduction. Review of regular languages. 2-Way Finite Automata accept the regular languages.

1 2 - T 1/10 DFA minimization and the Myhill-Nerode Theorem. Boolean logic.

1 3 - R 1/12 Myhill-Nerode to show languages not regular. Functions with no small circuits. Compactness for Boolean logic.

2 4 - T 1/17 First order logic: vocabulary, models, proofs; validity, satisfiability, etc.

2 5 - R 1/19 Review or recursive and r.e. sets, and their properties. Recursively inseparable pairs of languages.

3 6 - T 1/24 The completeness theorem and its consequences. (One hour class).

3 7 - R 1/26 The incompleteness theorem and its proof. Definition for various complexity classes. Linear speedup.

4 8 - T 1/31 Savitch's theorem. REACHABILITY in NL. Time and space hierarchy theorems and their consequences.

4 9 - R 2/1 Reductions and completeness. A provably intractable language. Time/space hierarchy theorems + consequences.

5 10 - T 2/7 REACHABILITY in coNL, NL=coNL, and its generalization. Complete problems for NL, P, and NP.

5 11 - R 2/9 NP-Completeness reductions: variants of SATISFIABILITY such as NAESAT.

6 12 - T 2/14 NP-Completeness reductions: graph-theoretic problems (3-COLORING, IND SET, HAM PATH)

6 13 - R 2/16 NP-Completeness reductions: TRIPARTITE MATCHING, SUBSET SUM. Strong & weak NPC. Decision vs. search.

7 14 - T 2/21 Finish decision vs. search. PSPACE-complete languges.

7 15 - R 2/23 Randomized complexity classes. Error reduction. PRIMES. Equality testing, arith circuit eval, checking matrix mult.

8 16 - T 2/28 Randomness, cont. Polynomial equality testing. UNDIRECTED CONNECTIVITY in RL. Universal traversal squences.

8 17 - R 3/2 Circuit families. BPP in P/poly. IP. Interactive proof for GRAPH NONISOMORPHISM. Start coNP in IP.

9 18 - T 3/7 Birds!! PSPACE in IP. Zero Knowledge. Zero-Knowledge.

9 19 - R 3/9 Perfect zero knowledge and PZK in envelope model for NP. MIP and its characterization. PCP and PCP theorem.

10 20 - R 3/14 Unapproximablity from the PCP theorem. More on PH. BPP in Sigma_2^p. Oracle separation results. Evaluations.

ECS 220 - Winter 2006 - List of Lecture Topics
Wk	Lect	Topic
0	1 - R 1/5	Introduction. Review of regular languages. 2-Way Finite Automata accept the regular languages.
1	2 - T 1/10	DFA minimization and the Myhill-Nerode Theorem. Boolean logic.
1	3 - R 1/12	Myhill-Nerode to show languages not regular. Functions with no small circuits. Compactness for Boolean logic.
2	4 - T 1/17	First order logic: vocabulary, models, proofs; validity, satisfiability, etc.
2	5 - R 1/19	Review or recursive and r.e. sets, and their properties. Recursively inseparable pairs of languages.
3	6 - T 1/24	The completeness theorem and its consequences. (One hour class).
3	7 - R 1/26	The incompleteness theorem and its proof. Definition for various complexity classes. Linear speedup.
4	8 - T 1/31	Savitch's theorem. REACHABILITY in NL. Time and space hierarchy theorems and their consequences.
4	9 - R 2/1	Reductions and completeness. A provably intractable language. Time/space hierarchy theorems + consequences.
5	10 - T 2/7	REACHABILITY in coNL, NL=coNL, and its generalization. Complete problems for NL, P, and NP.
5	11 - R 2/9	NP-Completeness reductions: variants of SATISFIABILITY such as NAESAT.
6	12 - T 2/14	NP-Completeness reductions: graph-theoretic problems (3-COLORING, IND SET, HAM PATH)
6	13 - R 2/16	NP-Completeness reductions: TRIPARTITE MATCHING, SUBSET SUM. Strong & weak NPC. Decision vs. search.
7	14 - T 2/21	Finish decision vs. search. PSPACE-complete languges.
7	15 - R 2/23	Randomized complexity classes. Error reduction. PRIMES. Equality testing, arith circuit eval, checking matrix mult.
8	16 - T 2/28	Randomness, cont. Polynomial equality testing. UNDIRECTED CONNECTIVITY in RL. Universal traversal squences.
8	17 - R 3/2	Circuit families. BPP in P/poly. IP. Interactive proof for GRAPH NONISOMORPHISM. Start coNP in IP.
9	18 - T 3/7	Birds!! PSPACE in IP. Zero Knowledge. Zero-Knowledge.
9	19 - R 3/9	Perfect zero knowledge and PZK in envelope model for NP. MIP and its characterization. PCP and PCP theorem.
10	20 - R 3/14	Unapproximablity from the PCP theorem. More on PH. BPP in Sigma_2^p. Oracle separation results. Evaluations.