ECS 120 – Theory of Computation

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ECS 120 – Fall 2012 – Phillip Rogaway – Lecture-by-lecture Course Outline

Week 0 Lect 01 R 9/27 Three problems of differing hardness. Strings and languages, and operators on them.

Week 1 Lect 02 T 10/2 Kleene closure. Homomorphisms. Example DFAs. Def of a DFA M. Def of L(M).

Lect 03 R 10/4 Minimal-size DFAs. L={aⁿbⁿ: n ≥ 0} has no DFA. Closure properties. Product construction.

Week 2 Lect 04 T 10/9 Quiz 1. Closure, properties, continued. NFAs and their languages. The subset construction.

Lect 05 R 10/11 Finish NFA/DFA equivalence. Regular languages and regular expressions.

Week 3 Lect 06 T 10/16 Regular languages = NFA-acceptable ones. Minimizing the number of states in a DFA.

Lect 07 R 10/18 Myhill-Nerode Thm. Ways to show languages not regular, incl. the PL. Decision procedures.

Week 4 Lect 08 T 10/23 Quiz 2. More decision algorithms on regular languages. Examples of CFGs. CFG terminology.

Lect 09 R 10/25 Formal defns of CFLs. Ambiguity. Regular languages are CF (two proofs). PDAs.

Week 5 Lect 10 T 10/30 Syntax for PDAs. Designing PDAs. PDAs accept the CFLs. Formalizing the language of a PDA.

Lect 11 R 11/01 CNF conversion efficiency. CFG membership. CYK algorithm. Pumping Lemma. Closure/nonclosure.

Lect aa U 11/04 Review session (217 Art, 7-8:30 pm)

Week 6 Lect 12 T 11/06 Midterm

Lect 13 R 11/08 Decision procedures for CFLs. Turing machines. Examples. Decidable and recognizable languages.

Week 7 Lect 14 T 11/13 Review: decidable, r.e. Entscheidungsproblem. TM variants/alterantives. The Church-Turing thesis.

Lect 15 R 11/15 NTMs, 2-tag systems. Arguments for/against C-T thesis. 4-Possiblities Thm. Undecidability of A_TM.

Week 8 Lect 16 T 11/20 Undecidability of A_TM. Many-one reductions. Examples: BTHP, FINITE, VIRUS.

Lect bb W 11/21 More example reductions worked out in discussion section.

Week 9 Lect 17 - T 11/27 Quiz 3. Lecture by Prof. Franklin. P, NP, and NP-Completeness. Strong Church-Turing thesis.

Lect 18 R 11/29 Review computability & Rice’s th. Review P, NP. REXPEQ, CIRCUIT-SAT, SAT, 3SAT, CLIQUE.

Week 10 Lect 19 - T 12/04 Def and meaning of NP-completness. Showing langauges NPC: 3SAT, CLIQUE. Cook-Levin Theorem.

Lect 20 R 12/06 More NPC rdxns: G3C, SUBSET SUM. Beyond P & NP: BPP, PSPACE, IP. Evaluations.

Lect cc - W 12/12 Review session. 1:00 - 2:30 pm, in Storer 1344.

Week 11 Lect dd - F 12/14 Final, 3:30-5:30 pm

ECS 120 – Fall 2012 – Phillip Rogaway – Lecture-by-lecture Course Outline
Week 0	Lect 01 R 9/27	Three problems of differing hardness. Strings and languages, and operators on them.
Week 1	Lect 02 T 10/2	Kleene closure. Homomorphisms. Example DFAs. Def of a DFA M. Def of L(M).
	Lect 03 R 10/4	Minimal-size DFAs. L={aⁿbⁿ: n ≥ 0} has no DFA. Closure properties. Product construction.
Week 2	Lect 04 T 10/9	Quiz 1. Closure, properties, continued. NFAs and their languages. The subset construction.
	Lect 05 R 10/11	Finish NFA/DFA equivalence. Regular languages and regular expressions.
Week 3	Lect 06 T 10/16	Regular languages = NFA-acceptable ones. Minimizing the number of states in a DFA.
	Lect 07 R 10/18	Myhill-Nerode Thm. Ways to show languages not regular, incl. the PL. Decision procedures.
Week 4	Lect 08 T 10/23	Quiz 2. More decision algorithms on regular languages. Examples of CFGs. CFG terminology.
	Lect 09 R 10/25	Formal defns of CFLs. Ambiguity. Regular languages are CF (two proofs). PDAs.
Week 5	Lect 10 T 10/30	Syntax for PDAs. Designing PDAs. PDAs accept the CFLs. Formalizing the language of a PDA.
	Lect 11 R 11/01	CNF conversion efficiency. CFG membership. CYK algorithm. Pumping Lemma. Closure/nonclosure.
	Lect aa U 11/04	Review session (217 Art, 7-8:30 pm)
Week 6	Lect 12 T 11/06	Midterm
	Lect 13 R 11/08	Decision procedures for CFLs. Turing machines. Examples. Decidable and recognizable languages.
Week 7	Lect 14 T 11/13	Review: decidable, r.e. Entscheidungsproblem. TM variants/alterantives. The Church-Turing thesis.
	Lect 15 R 11/15	NTMs, 2-tag systems. Arguments for/against C-T thesis. 4-Possiblities Thm. Undecidability of A_TM.
Week 8	Lect 16 T 11/20	Undecidability of A_TM. Many-one reductions. Examples: BTHP, FINITE, VIRUS.
	Lect bb W 11/21	More example reductions worked out in discussion section.
Week 9	Lect 17 - T 11/27	Quiz 3. Lecture by Prof. Franklin. P, NP, and NP-Completeness. Strong Church-Turing thesis.
	Lect 18 R 11/29	Review computability & Rice’s th. Review P, NP. REXPEQ, CIRCUIT-SAT, SAT, 3SAT, CLIQUE.
Week 10	Lect 19 - T 12/04	Def and meaning of NP-completness. Showing langauges NPC: 3SAT, CLIQUE. Cook-Levin Theorem.
	Lect 20 R 12/06	More NPC rdxns: G3C, SUBSET SUM. Beyond P & NP: BPP, PSPACE, IP. Evaluations.
	Lect cc - W 12/12	Review session. 1:00 - 2:30 pm, in Storer 1344.
Week 11	Lect dd - F 12/14	Final, 3:30-5:30 pm