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COMS W3261
Computer Science Theory
Fall 2015
  Class meets 1:10-2:25pm, Mondays and Wednesdays, room TBA.

First lecture is Wednesday, September 9, 2015.
 Teaching Staff
 Name   email   Office hours    Location 
Prof. Al Aho   aho@cs.columbia.edu   Mondays and Wednesdays 3:00-4:00pm   513 CSB
 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 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 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 W3137 Data Structures and Algorithms
  COMS W3203 Discrete Mathematics
 Schedule 2015
Date  Lecture  Reading 
Sep 9   1. Introduction to CS Theory  HMU, Ch. 1  
Sep 14   2. Finite Automata and Regular Languages HMU, Ch. 2 
Sep 16   3. Regular Expressions HMU, Ch. 2, Sects. 3.1, 3.3.1  
Sep 16   Homework Assignment #1 Due Sep 28  
Sep 21   4. Equivalence of Regular Expressions and Finite Automata HMU, Ch. 3  
Sep 23   5. Properties of Regular Languages HMU, Sect. 4.1, 4.2  
Sep 28   6. Decision Problems for Regular Languages HMU, Ch. 4 
Sep 30   7. Context-Free Grammars HMU, Ch. 5 
Sep 30   Homework Assignment #2 Due Oct 12 
Oct 5   8. Pushdown Automata HMU Ch. 6 
Oct 7   9. Equivalence of CFG's and PDA's HMU, Sect. 6.3 
Oct 12   10. CNF, Pumping Lemma, CYK Algorithm HMU, Ch. 7 
Oct 14   11. Closure and Decision Properties of CFL's HMU, Ch. 7 
Oct 14   Homework Assignment #3 Due Oct 26 
Oct 19   12. Turing Machines and Computability HMU, Ch. 8 
Oct 21   13. Variants of Turing Machines HMU, Ch. 8 
Oct 26   14. Algorithms and the Church-Turing Thesis HMU, Ch. 8 
Oct 28   15. The Diagonalization and Universal Languages HMU, Sects. 9.1-9.2 
Nov 2   Academic Holiday    
Nov 4   Midterm Lectures 1-15  
Nov 9   16. Undecidable Problems HMU, Ch. 9  
Nov 11   17. Post's Correspondence Problem HMU, Sects. 9.4-9.5 
Nov 11   Homework Assignment #4 Due Nov 23  
Nov 16   18. Complexity Theory; The Classes P and NP HMU, Sect. 10.1 
Nov 18   19. Satisfiability HMU, Sects. 10.2-10.3  
Nov 23   20. NP and co-NP HMU, Sect. 11.1 
Nov 25   Recitation  
Nov 30   21. Introduction to the Lambda Calculus  
Nov 30   Homework Assignment #5 Due Dec 9  
Dec 2   22. The Lambda Calculus II  
Dec 7   23. The Lambda Calculus III  
Dec 9   Final Review  
Dec 14   Final Exam Lectures 1-23  
 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.
 Class Policies
  Grading 15 % Best four homeworks out of five
40 % Midterm
45 % Final

aho@cs.columbia.edu Updated August 16, 2015