ECS 120 - Spring 2013 - List of Lecture Topics

Lecture Topic

Week 1 Lect 01 - M 3/31 Introduction. Three sample problems and their relative complexities. First language-theoretic defns: alphabets and strings.

Lect 02 - W 4/02 Languages and operators on them, including Kleene closure (star). Regular languages.

Disc 01 - W 4/02 PR. Hints on PS #1. Demonstrating langauges to be regular. Examples of DFAs and the languages they accept.

Lect 03 - F 4/04 More exampls of DFAs. Formalizing DFAs and their languages. Start closure properties of the DFA-acceptable languages.

Week 2 Lect 04 - M 4/07 Quiz 1. YZ: Closure properties of the DFA-acceptable languages. The product construction.

Lect 05 - W 4/09 More product-construction examples (union, intersection, set difference, symmetric differences). NFAs and their formalization.

Disc 02 - W 4/09 YZ. Course-material review. Problem set hints.

Lect 06 - F 4/11 Going over Q1. The DFA-acceptable languages are exactly the NFA-acceptable languages.

Week 3 Lect 07 - M 4/14 Using DFA/NFA equivalence to understand properties of this class. Showing DFAs minimal with the pigeonhole principle.

Lect 08 - W 4/16 Regular expression and well-definededness of their L operator. Regular languages are the DFA/NFA acceptable languagess.

Disc 03 - W 4/16 YZ. Examples: NFA to DFA conversion, NFA to regular expression conversion. Correctness of the latter procedure.

Lect 09 - F 4/18 The value of multiple characterizations. Showing languges not regular: PH arguments, closure properties, the pumping lemma.

Week 4 Lect 10 - M 4/21 More examples showing languages not regular. The Myhill-Nerode theorem.

Lect 11 - W 4/23 Quiz 2. Finish description and examples of the Myhill-Nerode theorem. DFA state minimization.

Disc 04 - W 4/23 YZ. Example of DFA state minimization, and the idea behind it. Q&A for homework and quiz problems.

Lect 12 - F 4/25 Regular-language decision questionsand their efficiency: equality, emptiness, finiteness, contains a palindrome.

Week 5 Lect 13 - M 4/28 Context free langauges: examples and definitions. Vocabulary, like yield, sentential form, deriviation. Ambiguity.

Lect 14 - W 5/01 Review. PDAs: examples and formalizations. Claimed equivalence of the CFLs and the PDA-acceptable langauges.

Disc 05 - W 5/01 YZ. Strategies for designing CFGs. Problem set hints. TA notes.

Lect 15 - F 5/02 Converting CFGs to PDAs. Chomsky normal form. A decision procedure for string membership in a CFG.

Week 6 Lect 16 - M 5/05 The pumping lemma for CFLs. Using the PL to show languages not regular. CFLs aren’t closed under complement.

Lect 17 - W 5/07 Closure and non-closure properties of the CFLs. Decision procedures for CFLs. Turing machines and their syntax.

Disc 06 - W 5/07 YZ. Converting a CFG into CNF. The CYK algorithm to decide if a string is in a CFL. Help for PS6. TA notes.

Lect 18 - F 5/09 Formalzing TMs. Turing-decidable (recusive) and Turing-acceptable (r.e.) languages. What shapes our scientific imagining.

Week 7 Lect 19 - M 5/12 Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm

Lect 20 - W 5/14 YZ. Altnernative models of computation: multitracks, multitapes, RAMs. The Church-Turing thesis. The four-possiblities theorem.

Disc 07 - W 5/15 No discussion section this week.

Lect 21 - F 5/16 More TM alternatives: RAMs, 2-tag systems and rule-110 CAs. Arguments for and against the CT Thesis.

Week 8 Lect 22 - M 5/19 Two views of NTMs and there equivalence to ordinary Turing machines. Encodings. Classification guesses.

Lect 23 - W 5/21 More language-classification guesses. Undecidability of A_TM. Defn of many-one reductions. A first rdxn: A_TM ≤_mHALT.

Disc 08 - W 5/21 Review of NTMs and their equivalence to DTMs. Practice with classification guesses. TA notes.

Lect 24 - F 5/23 Review. Turing reductions vs. many-one reductions. Practice doing many-one reductions. Tricks used: setting a clock, pre-accepting strings, dovetailing.

Week 9 Lect xx - M 5/26 Holiday — no class
Lect 25 - W 5/28 Quiz 3. YZ. Undecidability of the language CFGALL. TA notes.

Disc 09 - W 5/28 YZ: Finish proof of undecidability of CFGALL. Rice’s Theorem, proof, and its significance.

Lect 26 - F 5/30 DG: The classes P and NP. Alternative characterizations of NP. Example NP problems. P⊆NP.

Week 10 Lect 27 - M 6/02 NP-Completeness. Polynomial-time reductions, ≤_p. Definition of 3SAT. Showing 3SAT NP-complete.

Lect 28 - W 6/04 More examples of reductions and NP-Complete problems: CLIQUE, G3C, SUBSET SUM. Proof of the Cook-Leving theorem.

Disc 10 - W 6/04 More practice with NP-Completeness reductions: SUBSET SUM and VERTEX COVER.

Revi 01 - M 6/09 Review session in 106 Wellman from 3:30 pm to (roughly) 5:00 pm. Please work out the practice exam first.

Week 11 Lect xx - W 6/11 Final – 6:00 pm to 8:00 pm in our usual room

ECS 120 - Spring 2013 - List of Lecture Topics
	Lecture	Topic
Week 1	Lect 01 - M 3/31	Introduction. Three sample problems and their relative complexities. First language-theoretic defns: alphabets and strings.
	Lect 02 - W 4/02	Languages and operators on them, including Kleene closure (star). Regular languages.
	Disc 01 - W 4/02	PR. Hints on PS #1. Demonstrating langauges to be regular. Examples of DFAs and the languages they accept.
	Lect 03 - F 4/04	More exampls of DFAs. Formalizing DFAs and their languages. Start closure properties of the DFA-acceptable languages.
Week 2	Lect 04 - M 4/07	Quiz 1. YZ: Closure properties of the DFA-acceptable languages. The product construction.
	Lect 05 - W 4/09	More product-construction examples (union, intersection, set difference, symmetric differences). NFAs and their formalization.
	Disc 02 - W 4/09	YZ. Course-material review. Problem set hints.
	Lect 06 - F 4/11	Going over Q1. The DFA-acceptable languages are exactly the NFA-acceptable languages.
Week 3	Lect 07 - M 4/14	Using DFA/NFA equivalence to understand properties of this class. Showing DFAs minimal with the pigeonhole principle.
	Lect 08 - W 4/16	Regular expression and well-definededness of their L operator. Regular languages are the DFA/NFA acceptable languagess.
	Disc 03 - W 4/16	YZ. Examples: NFA to DFA conversion, NFA to regular expression conversion. Correctness of the latter procedure.
	Lect 09 - F 4/18	The value of multiple characterizations. Showing languges not regular: PH arguments, closure properties, the pumping lemma.
Week 4	Lect 10 - M 4/21	More examples showing languages not regular. The Myhill-Nerode theorem.
	Lect 11 - W 4/23	Quiz 2. Finish description and examples of the Myhill-Nerode theorem. DFA state minimization.
	Disc 04 - W 4/23	YZ. Example of DFA state minimization, and the idea behind it. Q&A for homework and quiz problems.
	Lect 12 - F 4/25	Regular-language decision questionsand their efficiency: equality, emptiness, finiteness, contains a palindrome.
Week 5	Lect 13 - M 4/28	Context free langauges: examples and definitions. Vocabulary, like yield, sentential form, deriviation. Ambiguity.
	Lect 14 - W 5/01	Review. PDAs: examples and formalizations. Claimed equivalence of the CFLs and the PDA-acceptable langauges.
	Disc 05 - W 5/01	YZ. Strategies for designing CFGs. Problem set hints. TA notes.
	Lect 15 - F 5/02	Converting CFGs to PDAs. Chomsky normal form. A decision procedure for string membership in a CFG.
Week 6	Lect 16 - M 5/05	The pumping lemma for CFLs. Using the PL to show languages not regular. CFLs aren’t closed under complement.
	Lect 17 - W 5/07	Closure and non-closure properties of the CFLs. Decision procedures for CFLs. Turing machines and their syntax.
	Disc 06 - W 5/07	YZ. Converting a CFG into CNF. The CYK algorithm to decide if a string is in a CFL. Help for PS6. TA notes.
	Lect 18 - F 5/09	Formalzing TMs. Turing-decidable (recusive) and Turing-acceptable (r.e.) languages. What shapes our scientific imagining.
Week 7	Lect 19 - M 5/12	Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm Midterm
	Lect 20 - W 5/14	YZ. Altnernative models of computation: multitracks, multitapes, RAMs. The Church-Turing thesis. The four-possiblities theorem.
	Disc 07 - W 5/15	No discussion section this week.
	Lect 21 - F 5/16	More TM alternatives: RAMs, 2-tag systems and rule-110 CAs. Arguments for and against the CT Thesis.
Week 8	Lect 22 - M 5/19	Two views of NTMs and there equivalence to ordinary Turing machines. Encodings. Classification guesses.
	Lect 23 - W 5/21	More language-classification guesses. Undecidability of A_TM. Defn of many-one reductions. A first rdxn: A_TM ≤_mHALT.
	Disc 08 - W 5/21	Review of NTMs and their equivalence to DTMs. Practice with classification guesses. TA notes.
	Lect 24 - F 5/23	Review. Turing reductions vs. many-one reductions. Practice doing many-one reductions. Tricks used: setting a clock, pre-accepting strings, dovetailing.
Week 9	Lect xx - M 5/26	Holiday — no class
	Lect 25 - W 5/28	Quiz 3. YZ. Undecidability of the language CFGALL. TA notes.
	Disc 09 - W 5/28	YZ: Finish proof of undecidability of CFGALL. Rice’s Theorem, proof, and its significance.
	Lect 26 - F 5/30	DG: The classes P and NP. Alternative characterizations of NP. Example NP problems. P⊆NP.
Week 10	Lect 27 - M 6/02	NP-Completeness. Polynomial-time reductions, ≤_p. Definition of 3SAT. Showing 3SAT NP-complete.
	Lect 28 - W 6/04	More examples of reductions and NP-Complete problems: CLIQUE, G3C, SUBSET SUM. Proof of the Cook-Leving theorem.
	Disc 10 - W 6/04	More practice with NP-Completeness reductions: SUBSET SUM and VERTEX COVER.
	Revi 01 - M 6/09	Review session in 106 Wellman from 3:30 pm to (roughly) 5:00 pm. Please work out the practice exam first.
Week 11	Lect xx - W 6/11	Final – 6:00 pm to 8:00 pm in our usual room