COMPSCI 501: Formal Language Theory

Spring 2019

Marius Minea

Welcome to the Spring 2019 homepage for COMPSCI 501: Formal Language Theory. Basic Information

Lectures: MWF 11:15 - 12:05, Goessman Lab 20
Instructor: Marius Minea (marius at cs), office: LGRC A261, office hours: Tue 1:30-2:30 pm
TA: Rik Sengupta (rsengupta at cs), office hours: Wed 6-7:30 pm, LGRT 220
Graders: Deeksha Razdan, Gourav Saha
Piazza page

Topics: COMPSCI 501 is an advanced undergraduate/master's-level core course in the theory of computation: formal language theory (finite automata, regular languages, context-free grammars and pushdown automata), computability theory, and complexity theory. This is a mathematical course: you will learn the main mathematical models of computation and how to prove their basic properties.

Prerequisites: COMPSCI 311, with a B- or better. It is useful to have "mathematical sophistication", at the level of of getting an A in COMPSCI 250, or in an upper-level math course.
These will have given you a broad view of some of the topics (automata and regular languages, fundamentals of NP-complete problems), but we will be able to look at these issues in-depth and of course cover much more advanced material.

Textbook (required): Michael Sipser, Introduction to the Theory of Computation, second or third edition.
This is an excellent book and we will follow it closely. It does a very good job of presenting the intuition first (including for proofs) before giving the rigorous treatment.

Homework

Homework 1 (LaTeX). Released 1/26/2019, due 2/7/2019, 11:59pm
Homework 2 (LaTeX). Released 2/12/2019, due 2/22/2019, 11:59pm
Homework 3 (LaTeX). Released 2/25/2019, due 3/7/2019, 11:59pm
Homework 4 (LaTeX). Released 3/8/2019, due 3/28/2019, 11:59pm
Homework 5 (LaTeX). Released 4/1/2019, due 4/12/2019, 11:59pm
Homework 6 (LaTeX). Released 4/16/2019, due 4/29/2019, 11:59pm

Grading:

Homework and quizzes: 40% (6 homeworks for 6% each, 4% for Moodle quizzes)
Midterm 1: 20% (Thu Feb 21, 7-9pm, ILC S131)
Midterm 2: 20% (Wed Apr 10, 7-9pm, ILC S131)
Final: 20% (Thu May 9, 10:30-12:30, Goessmann 20)
Exams have short questions, with credit split between the right answer and justification (balancing intuition and argumentation), plus 4-5 problems which require a full-fledged answer and proof.

Syllabus and schedule (tentative)

Week		Date	Topics	Readings
1	Lec 1	1/23	Introduction	Ch 0.1-0.4
	Lec 2	1/25	Deterministic Finite Automata (DFA)	Ch 1.1
2	Lec 3	1/28	Nondeterministic Finite Automata (NFA)	Ch 1.2
	Lec 4	1/30	Regular Expressions. Kleene's Theorem	Ch 1.3
	Lec 5	2/1	Nonegular Languages. Pumping Lemma	Ch 1.4
3	Lec 6	2/4	Myhill-Nerode Theorem
	Lec 7	2/6	Context-Free Grammars (CFG)	Ch 2.1
	Lec 8	2/8	Pushdown Automata (PDA)	Ch 2.2
4	Lec 9	2/11	Equivalence of CFGs and PDAs	Ch 2.2
	Lec 10	2/13	CFL Pumping Lemma	Ch 2.3
	Lec 11	2/15	Turing Machines (TM)	Ch 3.1
5	Lec 12	2/19	(Mon. schedule) Multi-tape and Nondeterministic TMs	Ch 3.2
	Lec 13	2/20	Algorithms and the Church-Turing Thesis	Ch 3.3
	Lec 14	2/22	Decidable Languages	Ch 4.1
6	Lec 15	2/25	Undecidability	Ch 4.2
	Lec 16 (Rik Sengupta)	2/27	Undecidable Problems in Formal Language Theory	Ch 5.1
	Lec 17 (Rik Sengupta)	3/1	Post Correspondence Problem	Ch 5.2
7	Lec 18	3/4	Reductions	Ch 5.3
	Lec 19	3/6	Recursion Theorem	Ch 6.1
	Lec 20	3/8	Descriptive Complexity	Ch 6.4
8	Lec 21	3/18	Time Complexity, Polynomial Time	Ch 7.1, 7.2
	Lec 22	3/20	Nondeterministic Polynomial Time (NP)	Ch 7.3
	Lec 23	3/22	NP-Completeness, Cook-Levin Theorem	Ch 7.4
9	Lec 24	3/25	More NP-Complete Problems	Ch 7.5
	Lec 25	3/27	The class PSPACE. Savitch's Theorem	Ch 8.1, 8.2
	Lec 26	3/29	Games and PSPACE-completentess	Ch 8.3
10	Lec 27	4/1	The classes L and NL / NL-completeness	Ch 8.4, 8.5
	Lec 28	4/3	NL equals co-NL	Ch 8.6
	Lec 29	4/5	Hierarchy Theorems	Ch 9.1
11	Lec 30	4/8	Review
	Lec 31	4/10	Circuit Complexity	Ch 9.3
	Lec 32	4/12	More Circuit Complexity	Ch 10.5
	Lec 33 (David Mix Barrington)	4/17	NC¹ and Barrington's Theorem
	Lec 34	4/19	Probabilistic Algorithms	Ch 10.2
13	Lec 35	4/22	Alternation	Ch 10.3
	Lec 36	4/24	Interactive Proof Systems	Ch 10.4
	Lec 37	4/26	Shamir's Theorem: IP=PSPACE	Ch 10.4
14	Lec 38	4/29	Cryptography	Ch 10.6
	Lec 39	5/1	Review

Last updated:5 November 2019