Theory of Computation, CSCI-UA.0453.001

Instructor. Richard Cole, 417 WWH, tel: 998-3119,

Class time. Mon/Wed 3:30-4:45pm., room 312 WWH.
First meeting:  Wednesday, September 3.

Exam Dates. Midterm: Wed. Oct 22.
Final: Wed. Dec 17, 4:00-5:50pm, room 202 WWH. Note room change.

Office hours. Mon/Thur 1-2pm and by appointment.

Mailing list, home page. There is a class mailing list (csci_0453_001_fa14). I send homework updates and other useful information to this list. You should be automatically subscribed to this list (if not see

Course Goal and Syllabus. The goal of this class is to develop your ability to evaluate and write mathematical claims in computer science, so as to be able to:

  •  Judge when a problem is solved (and equally important, when it is not yet solved).
  •  Explain such mathematical claims clearly and precisely.
  • Broadly speaking, this course will be studying what can and cannot be computed, and when something can be computed how simply can it be done. The specific topics covered will include proofs techniques, finite automata and regular languages, pushdown automata and context free languages, decidable and undecidable problems, and NP-completeness.

    Assignments. There will be more or less weekly homeworks. Late homeworks will not be accepted (except in the event of illness or other unavoidable circumstances). If for some reason you will be unable to hand in a homework on time, please discuss it with me beforehand.   While you may discuss homework problems with your fellow students, you must write up your solutions in your own words.  Be aware that you are unlikely to perform well on exams unless you gain practice at problem solving on the homeworks.

    Self-grading. On the day the homeworks are due I will be handing out solution sets. You are required to grade a copy of your homework using the solution set as a guide and to hand the graded copy in at the following class session. The self-grading should indicate the mistakes in the original solution and why they are mistakes. We will grade your original solution and your self-grading.  The purpose of this is to enhance your understanding of the material.

    To facilitate the management of the homework, I ask that you do the following.
    1. Write the solutions leaving space for your grading comments and for our grading comments (e.g. margins on both sides, and top and bottom, and don't use tightly spaced lines).
    2. Hand in you solution on Monday at the start of class. Hand in your self-graded solution on Wednesday, again, at the start of class.
    3. You may handwrite your homework, legibly of course, or typeset it. The best way to typeset mathematical material is to use Latex.

    Further Comments. If you are unable to completely solve a problem (or you cannot solve it at all) please write down your thoughts on how the problem should be approached, and where you approach breaks down. Or if you have given an answer that you know is incorrect, please indicate what the error is.

    Academic Integrity.  Please take note of  the course and departmental policy on this matter:

    Assessment. Homeworks will comprise 40% of the overall grade, the midterm 20% and the final 40%.  However, if the grade on the final is better than the midterm grade it will replace the midterm grade.  Exams will be closed book.

    Required text. The required text is the book I have been writing and teaching this course from for several years. Links to the chapters are below. The text is available for purchase from NYU Reprographics/Copy Central (547 La Guardia Place).  If you want a published textbook, you might consider: Michael Sipser, Introduction to the Theory of Computation, Thomson.  The most recent edition has the advantage of including solutions to a selection of problems. However, let me point out that the approach I will be taking diverges quite a bit from this text. Another possible text is: Daniel I.A. Cohen, Introduction to Computer Theory.  This text provides a lot of examples and can be quite helpful. However, it does not cover material for the whole course, and the approach it takes differs even more from the one I will be using in this course.

    Reading guide.   Basically, you should read my text. We will cover it in full.
    Here is a detailed lecture by lecture reading guide (this may get modified as the course proceeds).

    Homework Details. You may handwrite your homework, legibly of course, if you prefer, rather than typeset it.  In my experience, when typesetting, often too much effort is spent on the appearance of the homework and minor yet significant errors are overlooked.  Also, if your homework solution has multiple pages, please staple them; please don't fold down the corners or use paperclips, for the pages are much more likely to come apart. Finally, if handwriting, please use an easy to read ink color (blue or black, not red or green).

    Homeworks and handouts

    Course Content
    Chapter 1: Mathematical background
    Chapter 2: Finite Automata
    Chapter 3: Pushdown Automata
    Chapter 4: Decidability and Undecidability
    Chapter 5: NP Completeness
    Turing Machines

    Homework 1
    Homework 2
    Homework 3
    Homework 4
    Homework 5
    Homework 6
    Homework 7
    Homework 8
    Homework 9
    Homework 10
    Homework 11
    Homework 12
    Homework 13
    Homework 14

    Sample midterm 
    Sample final

    Last modified: December 10, 2014