ECS 120 - Spring 2010 - List of Lecture Topics

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

ECS 120 - Spring 2010 - List of Lecture Topics
	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