Lecture Schedule

This schedule is tentative and may change as the quarter progresses. I will try not to change scheduled days of quizzes and the midterm, however. [Note during pandemic: midterm replaced by shorter take-home quizzes.] The topics listed for each lecture are an estimate. After the lecture, I will alter the topics to reflect what we actually covered.

The reading assignment is to be done before lecture. In particular, the online Canvas reading quiz for a lecture will contain some questions about the reading assignment. If you're dismayed to notice that there is a reading assignment for the first lecture, there's no reading quiz before the first lecture. This reading is a review of discrete math (ECS 20), a prerequisite for this course, so I'm essentially just saying you should know that stuff already, but it's good to review just in case.

Any section/subsection in the lecture notes labeled "Optional" is something we will not cover. Topics from those sections will not appear on homework, quizzes, or exams.

Lecture 0 is not covered in class when teaching in person. It is a review of prerequisite discrete math concepts that will be used in the course. It will be covered in discussion the first week.

(pandemic edition)

I will pre-record lectures. You should watch these on your own. During the lecture period, I will be available on Zoom to take questions, but it will be less formal and more like office hours or review. I won't have much planned, since the planning I do for lecture is typically all in the content that I put in the videos.

Generally I've tried to break up each video into smaller chunks than a long 50-minute thing (although without interaction, most of these are 30-40 minutes instead of the full 50).

These videos are all linked from the AggieVideo playlist for this course. There are also playlists for each chapter:

• discrete math review (chapter 1)
• 1/2 (intro)
• 3 (DFAs)
• 4 (regex, CFG, NFA)
• 5 (closure properties)
• 6 (equivalence of regular language models)
• 7 (pumping lemma)
• 8 (Turing machines)
• 9 (polynomial time deciders, the class P)
• 10 (polynomial time verifiers and reductions, the class NP)
• 11 (undecidability)

There's a some errata in a few of the videos, which are explained at the pages at the links below with the individual videos.

lecture	date	videos	reading assignment	topics
0		1 sets 2 sequences 3 functions and relations 4 graphs and trees 5 Boolean logic 6 pigeonhole principle 7 combinatorics		discrete math review
1a	3/29	1 introduction to course 2 course policies 3 string theory	syllabus, 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, see also intro-slides.pdf Download intro-slides.pdf	introduction to theory of computation, course policies, string theory
1b	3/31	1 intuitive overview of DFAs 2 formal models of computation 3 formal definition of DFA syntax 4 intuitive overview of DFA semantics 5 examples of DFA state diagrams	3.1, 3.2, 3.3	intuitive introduction to deterministic finite automata (DFA), formal models of computation, formal definition of DFA syntax
1c	4/2	1 example DFAs deciding input length congruence 2 example DFA deciding binary number congruence 3 formal definition of DFA semantics	3.4, 3.5	more examples of DFAs, formal definition of DFA semantics
2a	4/5	1 regex introduction 2 regex formal definition 3 conventions and the tree view of regex's 4 small examples 5 example of regex matching double literals	4.1	regular expressions (regex)
2b	4/7	1 CFG introduction 2 formal definition of CFG syntax 3 formal definition of CFG semantics 4 right-regular grammars	4.2	context-free grammars (CFG)
2c	4/9	1 NFA introduction 2 formal definition of NFA syntax 3 example NFA and states it could reach 4 listing transitions versus defining transition function 5 formal definition of NFA semantics 6 ɛ-transition example	4.3	nondeterministic finite automata (NFA)
3a	4/12	1 automatic transformation of regex's NFAs, DFAs 2 roadmap for next two chapters 3 DFA union (product construction) example 4 DFA union proof	5.1, 5.2	introduction to closure properties, product construction, DFA closure properties for complement, ∪
3b	4/14	1 DFA intersection (two ways) 2 gotchas: multiple union or intersection, closure only goes one way, and difficulty of showing closure for concatenation and Kleene star 3 NFA union example 4 NFA concatenation example	5.3	DFA closure properties for ∩, NFA closure property examples
3c	4/16	1 NFA Kleene star example 2 NFA union proof 3 NFA concatenation proof 4 NFA Kleene star proof	5.3	NFA closure property proofs
4a	4/19	1 introduction to computational equivalence, NFAs can simulate DFAs 2 example of DFA simulating NFA (subset construction) 3 proof DFAs can simulate NFAs with no ε-transitions 4 handling ε-transitions 5 alternative choices in subset construction	6.1	equivalence of DFAs and NFAs  (subset construction)
4b	4/21	1 RRGs can simulate DFAs example 2 RRGs can simulate DFAs proof 3 NFAs can simulate RRGs proof 4 right-regular versus left-regular grammars	6.2	equivalence of RGs and NFAs
4c	4/23	1 NFAs can simulate regex's proof 2 NFAs can simulate regex's example 3 NFAs with "isolated" start and accept state 4 expression automata 5 regex's can simulate NFAs	6.3	equivalence of regex's and NFAs
5a	4/26	1 why we need rigor to argue that a language is not regular 2 direct proof that { x | #(0, x) = #(1, x) } is not regular 3 picture of previous proof 4 direct proof that { uu | u ∈ {0,1}* } is not regular	7.1	proving languages are not regular (Pumping Lemma)
5b	4/28	1 pumping lemma for regular languages 2 pumping lemma proof that {0n1n | n ∈ ℕ } is not regular 3 example of incorrect use of pumping lemma 4 pumping lemma proof that { x | #(0, x) = #(1, x) } is not regular 5 closure properties proof that { x | #(0, x) = #(1, x) } is not regular 6 pumping lemma proof that { uu | u ∈ {0,1}* } is not regular 7 pumping lemma proof that { 1n^2 | n ∈ ℕ } is not regular 8 pumping lemma proof that { 0i1j | i > j } is not regular 9 pumping lemma proof that { (01)n(10)n | n ∈ ℕ } is not regular	7.2, 7.3	using the pumping lemma
5c	4/30	1 introduction to Turing machines (TM) 2 example TM 3 formal definition of TM syntax 4 formal definition of TM semantics	8.1, 8.2, 8.3	introduction to Turing machines (TM), formal definition of TM syntax; formal definition of TM semantics
6a	5/3	1 languages decided/recognized by TMs 2 multitape TM transition function 3 single-tape TMs can simulate multitape TMs 4 other variants of TMs	8.5, 8.6	languages decided/recognized by TMs; variants of TMs
6b	5/5	no lecture (normally midterm exam would be on this day)
6c	5/7	1 TMs versus code 2 measuring running time 3 asymptotic analysis, definition of O() and o() 4 rules-of-thumb for comparing function growth rates 5 definition of Ω(), ω(), and Θ()	Appendix A, 9.1	asymptotic time analysis
7a	5/10	1 time complexity classes and the Time Hierarchy Theorem 2 definition of P, encoding of data structures 3 P is the same for most encodings and programming languages 4 example problem in P: Path	9.2, 9.4	the class P, analyzing running time of algorithms
7b	5/12	1 example problem in P: RelPrime 2 example problem in P: Connected 3 Optional: example problem in P: EulerianGraph 4 polynomial-time verifier for HamPath 5 polynomial-time verifier for Composites	9.5, 10.1	examples of problems in P, polynomial-time verifiers
7c	5/14	1 definition of NP 2 decision vs. search vs. optimization 3 example problem in NP: Clique 4 example problem in NP: SubsetSum 5 the P vs. NP question	10.2, 10.3	the class NP, search and optimization problems, examples of problems in NP, the P versus NP question
8a	5/17	1 exponential-time algorithms for NP problems 2 P versus NP versus EXP 3 introduction to NP-completeness and Boolean formulas 4 implementation in Python and the Boolean satisfiability problem 5 ranking the hardness of problems	10.4, 10.5, 10.6	exponential-time algorithms for NP problems, introduction to NP-completeness, motivation of polynomial-time reducibility
8b	5/19	1 reducing IndSet to Clique 2 definition of polynomial-time reducibility 3 using reductions to bound hardness of problems 4 how to remember which direction reductions go 5 definition of the 3SAT problem	10.6	polynomial-time reducibility, reduction of 3SAT to IndependentSet
8c	5/21	1 3SAT is reducible to IndSet 2 reduction between two problems is an algorithm, but it doesn't solve either problem 3 definition of NP-completeness 4 Cook-Levin Theorem: if P≠NP, then no NP-complete problem is in P	10.6, 10.7, 10.8	definition of NP-completeness, proving problems are NP-complete, Cook-Levin theorem
9a	5/24	1 halting problem definition and Turing-recognizability 2 reducibility 3 no-input halting problem is undecidable 4 recipe for showing undecidability	11.1,11.3	halting problem, reducibility
9b	5/26	1 acceptance problem is undecidable 2 empty language problem is undecidable 3 rejecting problem is undecidable 4 how to spot undecidability	11.3, 11.4	undecidable problems about algorithm behavior, how to spot undecidability
9c	5/28	1 comparing sizes of sets 2 ℕ vs. ℤ 3 ℕ vs. ℚ+ 4 ℕ vs. ℚ 5 ℕ vs. {0,1}* 6 ℝ vs. (0,1)	11.6	comparing sizes of sets
10a	5/31	Memorial Day
10b	6/2	1 diagonalization to show a set is smaller than its power set 2 the real numbers are uncountable and the Continuum Hypothesis 3 diagonalization to show the halting problem is undecidable	11.7	diagonalization, proof the halting problem is undecidable
10c	6/4	no lecture (start of final exam week)