ECS 120 - Spring 2013 - List of Lecture Topics |
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Lecture | Topic | ||
Week 1 | Lect 01 - M 4/01 | Introduction. Three sample problems and their relative complexities. Language-theoretic defns: alphabets, strings. | |
Lect 02 - W 4/03 | Operators on strings. Languages and operators on them, including Kleene closure. Relation of languages to decision/search. | ||
Disc 01 - W 4/03 | PR. Examples of DFAs. Views of their langauge. Formal definition of DFA syntax. Discussion of PS1 problems. | ||
Lect 03 - F 4/05 | Pigeonhole principle. Minimality. Def of δ*(q, x) and L(M). Closure under complement, union — the product construction. | ||
Week 2 | Lect 04 - M 4/08 | Closure under intersection, sym diff. Concatentation and Kleene closure? NFAs and their formalization. | |
Lect 05 - W 4/10 | Formalizing NFAs, cont. Quiz 1. Closure of the NFA-acceptable languages under concatenation and Kleene colosure. | ||
Disc 02 - W 4/10 | TP. Going over PS1 and Quiz 1. Questions on PS2. | ||
Lect 06 - F 4/12 | More on closure. NFA-acceptable languages = DFA-acceptable languages: the subset construction. Eliminating ε-arrows. | ||
Week 3 | Lect 07 - M 4/15 | Regular languages and regular expressions. Regular languages = DFA/NFA-acceptable languages. | |
Lect 08 - W 4/17 | Proving L=a^n b^n: n≥0} is not regular using the PH principle. The Myhill-Nerode theorem (warning: not in book). | ||
Disc 03 - W 4/17 | PR. More examples of Myhill-Nerode / DFA minimization. Questions on PS3. | ||
Lect 09 - F 4/19 | Reproving L=a^n b^n: n≥0} not regulary with the Myhill-Nerode theorem. The Pumping Lemma for regular languages. | ||
Week 4 | Lect 10 - M 4/22 | Classification examples: decide and prove if various languages are regular. Decision procedures involving regular languages. | |
Lect 11 - W 4/24 | Finish up decision procedures for regular languages. Quiz 2. | ||
Disc 04 - W 4/24 | PR. Questions on PS3. Discussed solutions to Quiz 2, which was miraculously returned. | ||
Lect 12 - F 4/26 | CFGs and CFLs: definitions and examples. Derivations. Parse trees. Leftmost derivations. Ambiguity. | ||
Week 5 | Lect 13 - M 4/29 | Review. Inherently ambiguous languages. CNF. Membership decision procedures (naive algorithm and CYK algorithm). | |
Lect 14 - W 5/02 | Putting CFGs into CNF. PDAs (pushdown automata): example, definitions, detailed example. | ||
Disc 05 - W 5/02 | PR. Homework help: a PDA for Problem 5.3. Example of the CYK algorithm. | ||
Lect 15 - F 5/03 | Dog Day! PDAs accept exactly the CFLs (proven in one direction only). The The pumping lemma for CFLs. | ||
Week 6 | Lect 16 - M 5/06 | Examples applications of the PL for CFLs. Closure properties (and non-closure properties) of the CFLs. | |
Lect 17 - W 5/08 | Finish closure properties of CFLs and decision procedures for them. Quiz 3. Description of Turing Machines. | ||
Lect 18 - F 5/10 | Formalizing TMs. Turing-decidable (rec) and Turing-acceptable (r.e.) languages. Building a TM. Return Q3. | ||
Week 7 | Lect 19 - M 5/13 | Review of notions. TM variants: multi-tracks, multi-heads, multi-tapes. Random-access machines (RAMs). | |
Lect 20 - W 5/15 | More models: 2-ctr machines, 2-tag systems, Rule 110. Church-Turing Thesis. Args for/against. 4-Possiblities Theorem. | ||
Disc 07 - W 5/16 | PR. Nondeterministic TMs. Example classifications under the 4-Possiblities Thm. Small-group discussions. | ||
Lect 21 - F 5/17 | PR dresses up. A_{TM} is undecidable. Definition of many-one reductions. Showing languages not rec / r.e. / co-r.e. | ||
Week 8 | Lect 22 - M 5/20 | Review of reductions. Practice doing reductions: undecidability of BTHP, FINITE, REG, VIRUS. | |
Lect 23 - W 5/22 | Two more reductions. Prizes for TM designs. Quiz 4. | ||
Disc 08 - W 5/22 | PR. Went over Quiz 4 and current problem set. Two more reductions: undecidability of CFGEQ and CFGΣ*. | ||
Lect 24 - F 5/24 | Self-referential programs. Using this to build a Trojan horse. The class P. Robustness and rationale for P. | ||
Week 9 | Lect xx - M 5/27 | Holiday — no class! Holiday — no class! Holiday — no class! Holiday — no class! Holiday — no class! | |
Lect 25 - W 5/29 | Guest lecture: Eric Griboff. Applications of DFAs (slides). Finite-state transducers (slides based on Thomas Hannforth). | ||
Disc 09 - W 5/29 | TP. More examples of reductions. Rice’s theorem. | ||
Lect 26 - F 5/31 | Review: P. The class NP. Langauges: SAT, 3SAT, CLIQUE. Poly-time reductions: ≤_{p}. A reduction: 3SAT≤_{p}CLIQUE. | ||
Week 10 | Lect 27 - M 6/03 | Definition and discussion of NP-Completeness and NP-harndess. G3C is NP-copmlete:3SAT≤_{p}G3C. | |
Lect 28 - W 6/05 | Proof of the Cook-Levin Theorem. Reductions from CIRCUIT-SAT to 3SAT. Student evaluations. | ||
Disc 10 - W 6/05 | PR. Going over the problem set that was just due. NP-completeness of SUBSET-SUM. | ||
Revi 01 - R 6/06 | PR. Review session: 6:10 pm in 1150 Hart. Please come having tried to solve at least the Spring 2004 final exam. | ||
Week 11 | Lect xx - S 6/08 | Final – 10:30 am to 12:30 pm in our usual room |