Calendar

• Reading: Chapter 0
• Handout 1, General Information
• Homework 1 out, due Day 4 at the beginning of class (PDF)

Recitation 1 (Day 2): Math Review

• Reading: Chapter 0
• Handout 2: Math Review (PDF)

• Deterministic Finite Automata (FA) and the languages they accept
• Reading: Section 1.1

Lecture 3 (Day 4): Nondeterministic Finite Automata

• Nondeterministic FA & languages they accept
• Equivalence of DFA and NFA
• Reading: Section 1.2
• Homework 1 due
• Homework 2 out, due Day 7 at the beginning of class (PDF)
• In general homework covers material covered up to and including the lecture in which it is handed out

 Recitation 2 (Day 5)

• Review of FA

Lecture 4 (Day 6): Regular Expressions

• Regular Expressions
• Lemma 1.29 (Regular expressions describe regular languages)
• Reading: Section 1.3

Lecture 5 (Day 7): More Regular Expressions

• Theorem 1.28, Lemma 1.32
• Homework 2 due
• Handout 3: Quiz practice problems (PDF)

Recitation 3 (Day 8)

• Review of regular languages, expressions
• Handout 4: Recitation Problems (PDF)

Lecture 6 (Day 9): End of Automata

• Non-regular languages
• Pumping Lemma
• Reading: Section 1.4

Lecture 7 (Day 10): Quiz 1

• Quiz 1 (PDF), in class
• Covers lectures 1 through 6
• Homework 3 (PDF) out, due Day 13

Recitation 4 (Day 11)

• Quiz Review

• Introduction to Turing Machines
• Church-Turing Thesis
• Multi-tape Turing Machines
• Reading: Chapter 3

Lecture 9 (Day 13): Non-determinism II

• Non-deterministic Turing Machines are no better
• Definition of Decidable Languages; Examples
• Reading: Section 4.1
• Homework 3 due
• Homework 4 out, due Day 16 (PDF)

Recitation 5 (Day 14)

• Turing Machines
• Handout 9: Recitation Problems (PDF)

Lecture 10 (Day 15): Undecidability

• The Halting Problem
• The Halting Problem is Undecidable
• Reading: Chapter 4.2

Lecture 11 (Day 16): Undecidability II

• Post Correspondence Problem is Undecidable
• Reading: Section 5.2
• Homework 4 due
• Homework 5 out, due Day 19 (PDF)

Recitation 6 (Day 17)

• Undecidability

Lecture 12 (Day 18): Undecidability III

• More Undecidable Problems
  o Counter Machines
     - Lecture I (page 269) of Kozen
  o The Game of Life (simulation to be found at http://www.math.com/students/wonders/life/life.html)

Lecture 13 (Day 19): Reductions

• Reductions and Mapping Reducibility
• Reading: Section 5.3
• Rice's Theorem: A photocopy of Lecture 34 from Kozen was passed out
• Homework 5 due

Recitation 7 (Day 20)

• Undecidability and Recursion

Lecture 14 (Day 21): End of Computabillity

• Computer Viruses and Undecidability

Lecture 15 (Day 22): Quiz 2

• Quiz 2, in class (PDF)
• Covers lectures 8 through 14
• Quiz 2a, a make-up test not given out in class (PDF)
• Homework 6 out, due Day 24 (PDF)

• Introduction to Complexity Theory
• Time Complexity
• The Class P
• Readings: Sections 7.1 - 7.2

Lecture 17 (Day 24): Nondeterministic Complexity

• The Class NP; Examples
• P vs. NP
• Reading: Section 7.3
• Homework 6 due
• Homework 7 out, due Day 26 (PDF)

Recitation 9 (Day 25)

• Complexity Classes

Lecture 18 (Day 26): NP-Completeness

• NP Completeness
• Poly-time Reducibility
• Reading: Section 7.4
• Homework 7 due
• Homework 8 out, due Day 29 (PDF)

Recitation 10 (Day 27)

• Reductions
• Handout 14 given out as problems (PDF)

Lecture 19 (Day 28): Cook-Levin Theorem

• Statement and Proof of Cook-Levin Theorem

Lecture 20 (Day 29): NP-Completeness II

• Additional NP-complete Problems
• Reading: Section 7.5
• Homework 8 due

Recitation 11 (Day 30)

• More on NP-completeness
• Handout 16 given out as problems (PDF)

Lecture 21 (Day 31): NP-Completeness III

• Additional NP-complete Problems

Lecture 22 (Day 32): Quiz 3

• Quiz 3, in class (PDF)
• Covers Lectures 16-21
• Homework 9 out, due Day 35 (PDF)
• Quiz 3a, a make-up test not given out in class (PDF)

Recitation 12 (Day 33)

• Optional lecture on Complexity Classes Beyond NP

• Probabilistic Algorithms
• More information about the Min-Cut algorithm can be found at http://www.cs.ucsd.edu/~russell/RANDCLASS/outline.html

Lecture 24 (Day 35): Randomness II

• Probabilistic Algorithms
• Handout from Randomized Algorithms (Motwani and Raghavan) given out in class. Extras in course drawer
• Additional material can be found in Section 2 of the scribe notes at http://icg.harvard.edu/~cs225/Scribenotes/
• Homework 9 due

Recitation 13 (Day 36)

• Probabilistic Algorithms
• Handout 18 given out as problems (PDF)

Lecture 25 (Day 37): Cryptography

• Cryptography and Complexity Theory
• Readings: Section 10.6, handout

Lecture 26 (Day 38): Cryptography II

• Cryptography and Complexity Theory

Recitation 14 (Day 39)

• Canceled!

Final Exam (Day 40)

• Final exam: 3 hours, 7 problems (PDF)