CS:4330 Theory of Computation, Spring 2018

This page gives highlights of past lectures and provides lecture notes, reading assignments, and exercises.

Chapters and sections in the readings are from the textbook, unless specified otherwise.

Dates	Topics	Readings
Jan 17	Course introduction and administration. Overview of course topics. Introduction to Automata, Computability, and Complexity Mathematical notions and Terminology Sets Sequences and tuples Functions and Relations Strings and languages	- Chap. 0 - Class notes 0
Jan 19	Regular Languages Finite Automata Regular Expressions	- Chap. 1 Sect. 1.1 Sect. 1.3 - Class notes 1
Jan 22	Nondeterministic finite automata From NFAs to DFAs	- Chap. 1 Sect. 1.2 - Class notes 2
Jan 24	Equivalences DFAs and NFAs Regular Expressions and finite automata	- Chap. 1 Sect. 1.2 Sect. 1.3 - Class notes 3
Jan 26	Equivalence between regular expressions and finite automata	- Chap. 1 Sect. 1.3 - Class notes 4
Jan 29	Pumping Lemma and nonregular languages	- Chap. 1 Sect. 1.4 - Class notes 5
Jan 31	Pumping Lemma and nonregular languages Introduction to Context-free Grammars	- Chap. 1 Sect. 1.4 - Class notes 5 - Chap. 2 Sect. 2.1 - Class notes 6
Feb 2	Context-free Grammars	- Chap. 2 Sect. 2.1 - Class notes 6
Feb 5	Chomsky Normal Form Pushdown Automata	- Chap. 2 Sect. 2.1 - Class notes 6 Sect. 2.2 - Class notes 7
Feb 7	Pushdown Automata	- Chap. 2 Sect. 2.2 - Class notes 7
Feb 9	Equivalence of PDAs and CFGs	- Chap. 2 Sect. 2.2 - Class notes 8
Feb 12	Non-context-free languages	- Chap. 2 Sect. 2.3 - Class notes 9
Feb 14	Deterministic context-free languages	- Chap. 2 Sect. 2.4 - Class notes 10
Feb 16	Deterministic context-free languages	- Chap. 2 Sect. 2.4 - Class notes 10
Feb 19	Turing Machines	- Chap. 3 Sect. 3.1 - Class notes 11
Feb 21	Turing Machines examples	- Chap. 3 Sect. 3.1 - Class notes 12
Feb 23	Turing Machines examples	- Chap. 3 Sect. 3.1 - Class notes 12
Feb 26	Turing Machines variants	- Chap. 3 Sect. 3.2 - Class notes 13
Feb 28	Turing Machines and Algorithms	- Chap. 3 Sect. 3.3 - Class notes 14
Mar 2	No lecture -- midterm 1
Mar 5	Decidable Languages	- Chap. 4 Sect. 4.1 - Class notes 15
Mar 7	Decidable Languages	- Chap. 4 Sect. 4.1 - Class notes 15 - Class notes 16
Mar 9	Undecidability	- Chap. 4 Sect. 4.2 - Class notes 17
Mar 19	Undecidability	- Chap. 4 Sect. 4.2 - Class notes 17
Mar 21	Reducibility	- Chap. 5 Sect. 5.1 - Class notes 18
Mar 23	Reducibility	- Chap. 5 Sect. 5.1 Sect. 5.3 - Class notes 19
Mar 25	Reducibility	- Chap. 5 Sect. 5.3 - Class notes 19
Mar 28	Decidability of Logical Theories Recommended readings: Satisfiability modulo theories	- Chap. 6 Sect. 6.2 - Class notes 20
Mar 30	Time Complexity	- Chap. 7 Sect. 7.1 - Class notes 21
Apr 2	The class P	- Chap. 7 Sect. 7.2 - Class notes 22
Apr 4	The class NP	- Chap. 7 Sect. 7.3 - Class notes 23
Apr 6	P versus NP and NP-completeness	- Chap. 7 Sect. 7.4 - Class notes 24
Apr 9	SAT is NP-hard Recommended readings: Handbook of Satisfiability	- Chap. 7 Sect. 7.4 - Class notes 24
Apr 11	Other NP-complete problems	- Chap. 7 Sect. 7.4 Sect. 7.5 - Class notes 25
Apr 13	No lecture -- midterm 2
Apr 15	Space complexity	- Chap. 8 Sect. 8.1 Sect. 8.2 Sect. 8.3 - Class notes 26
Apr 17	Space complexity	- Chap. 8 Sect. 8.1 Sect. 8.2 Sect. 8.3 - Class notes 26
Apr 19	Space complexity	- Chap. 8 Sect. 8.1 Sect. 8.2 Sect. 8.3 - Class notes 26
Apr 23	Other PSPACE-complete problems	- Chap. 8 Sect. 8.3 - Class notes 27
Apr 25	Sublinear space	- Chap. 8 Sect. 8.4 - Class notes 28
Apr 30	Summary for Automata and Languages	- Chap. 1-3 - Class notes 30
May 2	Summary for Computability Theory	- Chap. 3-5, Section 6.2 - Class notes 31
May 4	Summary for Complexity Theory	- Chap. 7-8 - Class notes 32

Lecture Notes