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COMS W3261
Computer Science Theory Section 001
Fall 2017
 Announcements
  Welcome to Computer Science Theory, Section 1, for Fall 2017!
This website contains all information relevant to the course.

Class meets 1:10-2:25pm, Mondays and Wednesdays, 428 Pupin.
First lecture is Wednesday, September 6, 2017.

Course webpage: https://www.cs.columbia.edu/~aho/cs3261
Columbia Courseworks: https://courseworks.columbia.edu
Piazza bulletin board: https://piazza.com/columbia/fall2017/comsw3261_001_2017_3/home
Course wiki: https://comsw3261-001-2017-3.wikispaces.columbia.edu/home

 Teaching Staff
 Name   email   Office hours    Location 
Prof. Al Aho   aho@cs.columbia.edu   Mon & Wed 3:00-4:00pm   513 CSB picture of Al Aho
 
Alexandre Lamy   all2187@columbia.edu   Thu 5:00-7:00pm   122 Mudd picture of Alexandre Lamy
Wendy Pan   wp2213@columbia.edu   Mon & Wed 11:30am-12:30pm   122 Mudd picture of Wendy Pan
Jianshuo Qiu   jq2253@columbia.edu   Thu 3:00-5:00pm   122 Mudd picture of Jianshuo Qiu
Zack Silber   zs2266@columbia.edu   Tue 4:00-6:00pm   122 Mudd picture of Zack Silber
Michael Tong   mct2159@columbia.edu   Wed 8:00-10:00am   122 Mudd picture of Michael Tong
Cindy Wang   xw2368@columbia.edu   Fri 4:00-6:00pm   122 Mudd picture of Cindy Wang
 
 Course Overview
  In Computer Science Theory you will learn computational thinking and get to know the fundamental models of computation that underlie modern computer hardware, software, and programming languages. You will also discover that there are limits on how quickly computers can solve some problems and that there are some problems that no computer can solve.

The course will cover the important formal languages in the Chomsky hierarchy -- the regular sets, the context-free languages, and the recursively enumerable sets -- as well as the formalisms that generate these languages and the machines that recognize them. The course will introduce the basic concepts of computability and complexity theory by focusing on the question, "What are the fundamental capabilities and limitations of computers?" The course will also introduce probably approximately correct learning, the model of computation underlying machine learning, and the untyped lambda calculus, the model of computation underlying functional programming languages.

The concepts covered in this course will be amply illustrated by applications to current programming languages, algorithms, natural language processing, and hardware and software design. The topics covered in Computer Science Theory are required background to many Computer Science upper division courses in programming languages, compilers, natural language processing, computer hardware and logic design, analysis of algorithms, computational complexity, learning theory, and cryptography.

 Pre- or Corequisites
  COMS W3134 or COMS W3137 Data Structures and Algorithms
  COMS W3203 Discrete Mathematics
 Schedule 2017
Date  Lecture  Reading 
Sep 6   1. Introduction to CS Theory  HMU, Ch. 1  
Sep 11   2. Finite Automata and Regular Languages   HMU, Ch. 2  
Sep 13   3. Regular Expressions   HMU, Sects. 3.1, 3.3.1  
Sep 18   4. Regular Expressions and Finite Automata   HMU, Ch. 3  
Sep 20   5. Properties of Regular Languages - I   HMU, Sects. 4.1 - 4.2  
Sep 25   6. Properties of Regular Languages - II   HMU, Ch. 4  
Sep 25   Homework Assignment #1   Due Oct 4 
Sep 27   7. Context-Free Grammars   HMU, Ch. 5 
Oct 2   8. Pushdown Automata   HMU, Ch. 6  
Oct 4   9. CFG's and PDA's   HMU Sects. 6.6, 7.1  
Oct 9   10. Pumping Lemma for CFL's   HMU, Ch. 7  
Oct 11   11. Properties of CFL's   HMU, Ch. 7  
Oct 11   Homework Assignment #2   Due Oct 19  
Oct 16   12. Turing Machines   HMU, Ch. 8  
Oct 18   13. TM Variants   HMU, Ch. 8  
Oct 23   14. Midterm Review   HMU, Chs. 1 - 7  
Oct 25   Midterm   HMU, Chs. 1 - 7  
Oct 30   15. The Diagonalization Language   HMU, Sects. 8.1.3, 9.1 - 9.3  
Oct 30   Homework Assignment #3   Due Nov 11  
Nov 1   16. The Universal Language   HMU, Sect. 9.2 
Nov 6   Academic Holiday  
Nov 8   17. Post's Correspondence Problem   HMU, Sects. 9.4 - 9.5  
Nov 13   18. Undecidable Problems   HMU, Ch. 9  
Nov 13   Homework Assignment #4   Due Nov 22  
Nov 15   19. The Classes P and NP   HMU, Sects. 10.1, 10.2.1 
Nov 20   20. Satisfiability is NP-complete   HMU, Sects. 10.1-10.3  
Nov 22   21. Restricted Satisfiability Problems   HMU, Sect. 10.3 
Nov 27   22. Introduction to PAC Learning   Aaronson: Lecture Notes 19&20  
Nov 29   Homework Assignment #5   Due Dec 11  
Nov 29   23. The Lambda Calculus I   Edwards: The Lambda Calculus  
Dec 4   24. The Lambda Calculus II   Edwards: The Lambda Calculus  
Dec 6   25. The Lambda Calculus III   Edwards: The Lambda Calculus  
Dec 11   26. Final Review   Lectures 12-25 
Dec 18?   Final Exam Lectures 12-25  
 Required Text
  John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman
Introduction to Automata Theory, Languages, and Computation, Third Edition
Pearson/Addison-Wesley, 2007, ISBN 0-321-45536-3
 Additional References
  Michael Sipser
Introduction to the Theory of Computation, Third Edition
Cengage Learning, 2013

  Alfred V. Aho and Jeffrey D. Ullman
Foundations of Computer Science, C Edition
W. H. Freeman, 1995
An online version of this book is available here.
  Scott Aaronson and Nancy Lynch
6.045J Automata, Computability, and Complexity, Spring 2011
MIT OpenCourseWare
 Class Policies
  Grading 15 % Best four out of five homeworks
40 % Midterm
45 % Final
  Homeworks Five problem sets will be assigned during the semester. Follow the detailed instructions on each problem set.
Post your solutions to each problem set on Courseworks/COMSW3261/Assignments on or before each due date.
Each problem set is worth 100 points and only the four best of your five problem sets will be counted. The aggregate score of these four assignments will constitute 15% of your final grade.
Since only four out five assignments will be counted, this policy will allow you to skip one problem set for whatever reason you choose. Late assignments will not be accepted.
You must write your solutions in your own words by yourself. You can consult the instructor, the TAs, or your fellow students for help but you must acknowledge any sources you use other than yourself on your answers.
You are expected to adhere to the Academic Honesty Policy of the Department of Computer Science.

aho@cs.columbia.edu Updated September 19, 2017