ECS 120 - Spring 2010 - List of Lecture Topics |
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Lecture | Topic | ||
Week 1 | Lect 01 - M 3/29 | Introduction. Three sample problems and their relative complexities. Language-theoretic definitions: alphabets, strings, languages. | |
Lect 02 - M 3/29 | (Discussion section.) Operators on strings and languages: concatenation, reversal, union, intersection, complement, star (Kleene closure). Examples. | ||
Lect 03 - W 3/31 | Finish operators: various examples, and L^+. DFAs Examples and practice. Formal definition of a DFA and the language one accepts. | ||
Lect 04 - F 4/02 | Warning on well-definindedness. An inductive proof, a pigeonhole proof. Closure properties. DFA-acc languages are closed under complement. | ||
Week 2 | Lect 05 - M 4/05 | Classes of languages. Product construction: closure of the DFA-acc languages under union, intersection. NFAs. Closure under union. | |
Lect 06 - W 4/07 | Formalization of NFAs. More closure properties. Start showing the NFA-acceptable languages are DFA-acceptable. | ||
Lect 07 - F 4/09 | Finish showing DFA-acceptable languages = NFA acceptable languages. Regular languages and their representation by regular expressions. | ||
Week 3 | Lect 08 - M 4/12 | Prof. Vladimir Filkov lectures: the regular languages are exactly the NFA-acceptable ones. GNFAs (as a clever proof technique). | |
Lect 09 - W 4/14 | Quiz 1. Prof. Vladimir Filkov lectures: Proving languages not regular: the pumping lemma for regular languages. | ||
Lect 10 - F 4/16 | Strong form of pumping lemma. Examples of proving various languages not regular using the pumping lemma or closure properties. | ||
Week 4 | Lect 11 - M 4/19 | Decision procedures and polynomiality. Deciding questions concerning regular languages and whether or not they are polynomial time. | |
Lect 12 - W 4/21 | A last algorithm: a cute counting problem [some prepared notes on it]. Start CFLs: first examples and basic terminology. | . | |
Lect 13 - F 4/23 | Formal definitions for CFLs: CFGs, derivations, parse trees, ambiguity. Designing a CFG (ex: L={x#y: x, y distinct binary strings}). | ||
Week 5 | Lect 14 - M 4/26 | Finishing our tricky CFG example. The language-membership decision question for CFLs. Chomsky Normal Form (CNF). | |
Lect 15 - W 4/28 | PDAs: picture, syntax, examples, and a formal definition of the language that a PDA accepts. | ||
Lect 16 - F 4/30 | A last PDA example. The PDA-acceptable languages are exactly the CFLs. A pumping lemma for CFLs. | ||
Week 6 | Lect 17 - M 5/03 | Practice using the pumping lemma. Proving languages not context free. Closure and non-closure properties of the CFLs. | |
Lect xx - T 5/04 | Midterm Review session 6:10–7:30 pm in 217 Art. Work out the the practice midterm before coming. | ||
Lect 18 - W 5/05 | :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Midterm :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: | ||
Lect 19 - F 5/07 | Anhad Singh lecturing. Turing machines: examples and formalization. Turing-decidable (recursive) and Turing-acceptable (r.e.) languages. | ||
Week 7 | Lect 20 - M 5/10 | Review of TM-related notions. Turing-machine variants: two-way infinite tapes, multiple heads, ... | |
Lect 21 - W 5/12 | More TM variants, including unrestricted grammars, RAMs, and NTMs. The Church-Turing and Digital Modeling Theses. | ||
Lect 22 - F 5/14 | MT discussion. Arguments for and against the Church-Turing and Digital-Modeling Thesis. The Four-Possibilities theorem. | ||
Week 8 | Lect 23 - M 5/17 | Classification guesses: re, co-re, decidable, neither. Undecidability of Atm. Significance of this result. | |
Lect 24 - W 5/19 | Reducibility: definition and properties of many-one reductions. Using reductions in a first example (the language EMPTY). | ||
Lect 25 - F 5/21 | Quiz 2. Practice doing reductions (you need to learn this skill). | ||
Week 9 | Lect 26 - M 5/24 | More undecidable problems: VIRUS-DETECTION (does program P try to erase your disk?). CFGALL (is L(G)=Σ*, for CFG G?). PCP. | |
Lect 27 - W 5/26 | Complexity theory: the classes P and NP. Example languages and where they fall. | ||
Lect 28 - F 5/28 | Polynomial-time reductions. The notion of NP-completeness. The Cook-Levin theorem. Sample reductions. | ||
Week 10 | Lect xx - M 5/31 | Holiday — no class and no discussion section | |
Lect 29 - W 6/02 | Proof of the Cook-Levin theorem. Another reduction: CLIQUE is NP complete. Student evaluations. | ||
Lect xx - F 6/04 | No, there is no lecture 30, it was been stolen by Mrak. Today be dead day. Greetings, fellow zombies. | ||
Lect xx - F 6/04 | Review session for the final: 2:10–4:00 in our usual room (2016 Haring). | ||
Week 11 | Lect xx - M 6/07 | Final – 8 am, argggg |