ECS 120 - Spring 2013 - List of Lecture Topics

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≤_pCLIQUE.

Week 10 Lect 27 - M 6/03 Definition and discussion of NP-Completeness and NP-harndess. G3C is NP-copmlete:3SAT≤_pG3C.

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

ECS 120 - Spring 2013 - List of Lecture Topics
	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≤_pCLIQUE.
Week 10	Lect 27 - M 6/03	Definition and discussion of NP-Completeness and NP-harndess. G3C is NP-copmlete:3SAT≤_pG3C.
	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