ECS 220 - Winter 2006 - List of Lecture Topics |
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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. |