Syllabus

- Jan. 26 and Jan. 28: Introduction, review basic concepts and proofs, Textbook Chapter 0. Slides

- Feb. 2 and Feb. 4: DFA and regular language, designing DFAs, closure under union, Textbook Chapter 1.1.

- Feb. 9 and Feb. 11: NFA and equivalence to DFA, closure under concatenation, Textbook Chapter 1.2.

- Feb. 16 and Feb. 18: Closure under star, regular expressions and their equivalence to DFA, Textbook Chapter 1.2 and 1.3.

- Feb. 23 and Feb. 25: Finishig regular expressions and their equivalence to DFA, pumping lemma and non-regular languages, Textbook Chapter 1.3 and 1.4.

- Mar. 2: Decision problems of regular languages, Textbook Chapter 4.1. DFA minimization.

- Mar. 9 and Mar. 11: Basics of context free languages, starting designing context free grammar, Textbook Chapter 2.1.

- Mar. 16 and Mar. 18: Designing context free grammar, Pumping Lemma for CFL, Textbook Chapter 2.1 and 2.3.

- Mar. 23 and Mar. 25: Pumping Lemma for CFL, starting Turing Machine. Textbook Chapter 2.3 and 3.1.

- Apr. 6 and Apr. 8: Variants of Turing Machines, starting decidability. Textbook 3.2, 4.2

- Apr. 13 and Apr. 15: Undecidable and unrecognizable languages, mapping reduction, starting time complexity, P and NP. Textbook Chapter 4.2, 5.1, 5.3, 7.2, 7.3.

- Apr. 20: Polynomial time reduction, NP-completeness, start Cook-Levin Theorem. Textbook Chapter 7.2, 7.3, 7.4.

- Apr. 27 and Apr. 29: More NP-complete problems, decision vs search, conclusion of class. Textbook Chapter 7.5.

### Assignments

- Writing 1 Homework 1

- Writing 2 Homework 2

- Writing 3 Homework 3

- Midterm 1 practice problems

- Writing 4 Homework 4

- Writing 5 Homework 5

- Midterm 2 practice problems

- Writing 6 Homework 6

- Writing 7 Homework 7

- Final exam practice problems

### Further readings

**Introduction to mathematical arguments**

**Some Help on Reading Mathematics and Creating Proofs**

**An article about Alan Turing**

**A website about Turing and the history of modern computing**

**Godel's letter to von Neumann**

**Clay Institute's official page about the P vs. NP problem**

Lance Fortnow's exposition of the P vs. NP problem

- Writing 1 Homework 1