Last year’s list of lectures, and a list from Fall 2012 (includes videos).
ECS 120 - Spring 2015 - List of Lecture Topics |
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Lecture | Topic | ||
Week 1 | Lect 01 - M 3/30 | Introduction. Three sample problems and their relative complexities. First language-theoretic defns: alphabets and strings. | |
Lect 02 - W 4/01 | Strings and operations on them. Languages and operators on them, including Kleene closure (star). | ||
Disc 01 - W 4/01 | PR. Hints on PS #1. More operations on languages. First examples of DFAs and the languages they accept. | ||
Lect 03 - F 4/03 | More exampls of DFAs. Different view of the language of a DFA M. Formalizing DFAs and their languages. | ||
Week 2 | Lect 04 - M 4/06 | Closure properties of the DFA-acceptable languages. The product construction. Definition of an NFA. | |
Lect 05 - W 4/08 | Defining the language of an NFA. Closure properties for the NFA-acceptable languages. | ||
Disc 02 - W 4/08 | Definition review, practice with making DFAs, Kleene closure (star). Aaron’s notes. | ||
Lect 06 - F 4/10 | Quiz 1. Consequences of DFA/NFA equivalence on closure properties. Proof of DFA/NFA equivalence. | ||
Week 3 | Lect 07 - M 4/13 | Finish DFA/NFA equivalence. Showing DFAs of minimal size using the pigeonhole principle. The Myhill-Nerode theorem. | |
Lect 08 - W 4/15 | Restatement and proof of (some of) the Myhill-Nerode theorem. Algorithm for DFA minimization. | ||
Disc 03 - W 4/15 | Review of: subset construction, equivalence classes, and DFA minimization. | ||
Lect 09 - F 4/17 | Regular languages and regular expressions. Regular languages = DFA/NFA acceptable ones. | ||
Week 4 | Lect 10 - M 4/20 | Methods for showing languages not regular, including the pumping lemma. | |
Lect 11 - W 4/22 | Using closure properties to show languages not regular. decision procedures for regular langauges and their efficiency | ||
Disc 04 - W 4/22 | Review: pumping lemma, nonregular languages, and decision procedures. Aaron’s notes. | ||
Lect 12 - F 4/24 | CFLs and CFGs: examples and definitions. Ambiguity. | ||
Week 5 | Lect 13 - M 4/27 | Aaron lecturing. More on ambiguity. Inherently ambiguous languages. PDAs. CFG to PDA conversion. | |
Exam 1 - W 4/29 | Midterm | ||
Lect 14 - W 4/29 | No discussion section this week. | ||
Lect 15 - F 5/01 | Review of CFLs. Converting a CFG into Chomsky Normal Form (CNF). The CYK Algorithm for CFG membership. | ||
Week 6 | Lect 16 - M 5/04 | Showing languages not context free: a pumping lemma. Closure and non-closure properties. | |
Lect 17 - W 5/06 | More on CFLs closure properties. Decision questions on CFLs. Idea of a Turing machine. A book Turing read as a child. | ||
Disc 06 - W 5/06 | Examples of CNF conversion, the CYK algorithm, and using the pumping lemma for CFLs. | ||
Lect 18 - F 5/08 | Programming a TM. Formalization of a TM as a 7-tuple. Definitions of a TM deciding and accepting a language. | ||
Week 7 | Lect 19 - M 5/11 | Turing decidable (recursive) and Turing acceptable (r.e.) langauges. TM variants. RAMs. | |
Lect 20 - W 5/13 | Finish alternative models of computation. The Church-Turing thesis. (Know what this says!) Arguments for and against. | ||
Disc 07 - W 5/13 | Unrestricted grammars generate exactly the r.e. languages. Undecidablity of the halting problem, HALT. Aaron’s notes | ||
Lect 21 - F 5/15 | Quiz 2. Luis Esparza (Program Coordinator at ICC): Finding jobs and internships. | ||
Week 8 | Lect 22 - M 5/18 | Finish Church-Turing thesis. The four-possiblities theorem. Encodings. Classification guesses. | |
Lect 23 - W 5/20 | PS7 awards. Undecidability of ATM. Definition and properties of many-one reductions, the ≤m relation. | ||
Disc 08 - W 5/20 | Classification guesses. Many-one reductions: HALT ≤m ATM and ATM ≤m REGULAR. | ||
Lect 24 - F 5/22 | Examples of many-one reductions to show problems undecidable, not r.e., or not co-r.e. | ||
Week 9 | Lect xx - M 5/25 | Holiday — no class | |
Lect 25 - W 5/27 | More examples of reductions. Dovetailing. Rice’s theorem. Undecidability of L(G)=Σ* for a CFG G. | ||
Disc 09 - W 5/27 | Finish ATM ≤m CFGALL. Proof of Rice’s Theorem. Uncountability of the set of all languages. Aaaron’s notes | ||
Lect 26 - F 5/29 | Defs of P and NP. SAT, CFGALL, DFAALL, DIOPHANTINE, G3C. Defs of ≤p and NPC. | ||
Week 10 | Lect 27 - M 6/01 | Review of complexity theory. How to show a language NPC. Cook-Levin theorem. NP completeness of 3SAT and G3C. | |
Lect 28 - W 6/03 | Proof of the Cook-Levin Theorem. Another NPC result: SUBSETSUM. Course evaluations. | ||
Disc 10 - W 6/03 | Finish SUBSETSUM reduction. More polynomial-time reductions. Aaaron’s notes | ||
Revi 01 - F 6/05 | Review session | ||
Week 11 | Lect xx - m 6/08 | Final – 3:30 pm in our usual room (1003 Giedt) |