CS 332: Elements of the Theory of Computation, Fall 2021
This course is an introduction to the theory of computation. This is the branch of computer science that aims to understand which problems can be solved using computational devices and how efficiently those problems can be solved. To be able to make precise statements and rigorous arguments, computational devices are modeled using abstract mathematical "models of computation." The learning objectives of the course are to:
- Foremost, understand how to rigorously reason about computation through the use of abstract, formal models.
- Learn the definitions of several specific models of computation including finite automata, context-free grammars, and Turing machines, learn tools for analyzing their power and limitations, and understand how they are used in other areas of computer science.
- Learn how fundamental philosophical questions about the nature of computation (Are there problems which cannot be solved by computers? Can every problem for which we can quickly verify a solution also be solved efficiently?) can be formalized as precise mathematical problems.
- Gain experience with creative mathematical problem solving and develop the ability to write correct, clear, and concise mathematical proofs.
||Mark Bun, mbun [at] bu [dot] edu
|Instr. Office Hours:
||Mon 5:00-6:00 PM (MCS 114)
||Fri 5:00-6:00 PM (MCS 114)
||Islam Faisal, islam [at] bu [dot] edu
|TF Office Hours:
||Tue 5:00-6:00 PM (MCS B21)
||Thu 4:00-5:00 PM (MCS B21)
||Tue, Thu 2:00-3:15 PM (EPC 209)
||Wed 11:15-12:05 AM (MCS B31)
||Wed 12:20-1:10 PM (KCB 104)
Course Website: https://cs-people.bu.edu/mbun/courses/332_F21. The website contains the course syllabus, schedule with assigned readings, homework assignments, and other course materials.
Piazza: https://piazza.com/bu/fall2021/cs332. All class announcements will be made through Piazza, so please set your notifications appropriately. Please post questions about the course material to Piazza instead of emailing the course staff directly. It is likely that other students will have the same questions as you and may be able to provide answers in a more timely fashion. Active participation on Piazza may add extra points to your participation grade.
Gradescope: https://gradescope.com. Sign up for a student account on Gradescope using your BU email address. The entry code for the course is 2RYZ3P. Homework assignments are to be submitted to Gradescope in PDF format.
The basic concepts of the theory of computation are studied. Topics include models of computation, polynomial time, Church's thesis; universal algorithms, undecidability and intractability; time and space complexity, nondeterminism, probabilistic computation and reductions of computational problems.
CS 131 (Combinatoric Structures) and CS 330 (Introduction to Algorithms). If you have not completed the prerequisites for the course, please schedule a meeting with me before registering.
- Automata and Formal Language Theory. Deterministic finite automata, nondeterministic finite automata, regular expressions. Non-regular languages. Context-free grammars.
- Computability Theory. Turing Machines and the Church-Turing thesis. Decidability, halting problem. Reductions.
- Complexity Theory. Time complexity, space complexity, hierarchy theorems. Complexity classes P, NP, PSPACE and the P vs. NP question. Polynomial time reductions and NP-completeness.
(Perpetually Tentative) Schedule
||Sipser 0, Lec01, Lec01-ann
||Collaboration and Honesty Policy, Math & Algorithms Review, HW0 out
||Sets, strings, and languages
||Sipser 0, Lec02, Lec02-ann
||L2 polls, HW 0 due, HW1 out
||Sipser 1.1-1.2, Lec03, Lec03-ann
||L3 polls, Automata Tutor
||DFA-NFA equivalence, regular operations
||Sipser 1.2, Lec04, Lec04-ann
||L4 polls, HW 1 due, HW2 out
||Closure properties, regular expressions
||Sipser 1.2-1.3, Lec05, Lec05-ann
||Regular expressions vs. FAs, distinguishable sets
||Sipser 1.3, Lec06, Lec06-ann, Myhill-Nerode
||L6 polls, HW 2 due, HW3 out
||Lec07, Lec07-ann, Myhill-Nerode
||Test 1 Review
||Lec08 (no annotations)
||No polls, HW 3 due
||Test 1 (in-class portion)
||Sipser 3.1, 3.3, Lec09, Lec09-ann
||L9 polls, TM simulator, A real TM, Test 1 due (take-home portion), HW4 out
||TM variants and examples
||Sipser 3.2, Lec10, Lec10-ann
||NO CLASS — Indigenous Peoples' Day (Monday schedule of classes)
||HW 4 due, HW5 out
||Closure properties, nondeterminism, Church-Turing thesis
||Sipser 3.2, Lec11, Lec11-ann
||Decidable languages, Universal TM
||Sipser 4.1, Lec12, Lec12-ann
||L12 polls, HW 5 due, HW6 out, universal_TM.py
||Diagonalization, undecidability, unrecognizability
||Sipser 4.2, Lec13, Lec13-ann
||More undecidability, reductions
||Sipser 4.2, 5.1, Lec14, Lec14-ann
||L14 polls, HW 6 due, HW7 out
||Sipser 5.1, Lec15, Lec15-ann
||Test 2 Review
||HW 7 due
||Test 2 (in-class portion)
||Sipser 5.3, Lec17, Lec17-ann
||L17 polls, Test 2 (take-home portion) due, HW8 out
||Time complexity, space complexity
||Sipser 7.1, 8.0, Lec18, Lec18-ann
||Hierarchy theorems, complexity class P
||Sipser 9.1, 7.2, Lec19, Lec19-ann
||L19 polls, HW 8 due, HW9 out
||More P, nondeterminsitic time, NP
||Sipser 7.2-7.3, Lec20, Lec20-ann
||More on NP
||Sipser 7.3-7.4, Lec21, Lec21-ann
||L21 polls, HW 9 due
||NO CLASS — Happy Thanksgiving!
||Sipser 7.4-7.5, Lec22, Lec22-ann
||L22 polls, HW10 out
||Sipser 7.4-7.5, Lec23, Lec23-ann
||Sipser 8.1-8.2, Lec24, Lec24-ann
||Course Wrap-Up and Final Review
||HW 10 due
||Final Exam (in-class portion), 3-5 EPC 209
||Final exam (take-home portion) due
Texts and References
Michael Sipser, Introduction to the Theory of Computation, 3rd Edition. ISBN-13: 978-1133187790.
for a list of errata.
Reading the textbook before class and reviewing it after class are important for solidifying your understanding of the course material. However, I do not want the exhorbitant price of the book to pose a barrier to your learning. Using an older edition of the text is fine (though beware that section numbers may be different). If the cost of the textbook still presents a burden for you, let me know and I can loan you a copy or recommend another solution.
Richard Hammack, Book of Proof. Available online here.
Automata and Computability Theory:
Dexter Kozen, Automata and Computability.
Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach.
Cristopher Moore and Stephan Mertens, The Nature of Computation.
Your grade in the course will be determined by homework assignments, three take-home tests, and class participation.
The following letter grades are guaranteed if you earn the corresponding percentages: A ≥90%, A- ≥85%, B+ ≥80%, B ≥75%, B- ≥70%, C+ ≥65%, C ≥60%. However, to correct for the possibility of assignments and exams being more difficult than anticipated, letter grades may be (significantly) increased above these guarantees.
There will be weekly homework assignments to be submitted on Gradescope most Tuesdays at 11:59PM. No late homework will be accepted. To accomodate extenuating circumstances, your lowest homework grade will be dropped.
You are allowed, and indeed encouraged, to collaborate with other students on solving the homework problems. However, you must write the solutions independently in your own words. Details of the collaboration policy may be found here: Collaboration and Honesty Policy
Some homework assignments may include optional "bonus" problems. Solving these problems will not directly contribute to your homework grade but may improve the letter grade you receive in the course if the final percentage we calculate is on the borderline between two letter grades. Solving bonus problems is also a good way to impress your instructor if you are seeking a recommendation letter, research opportunities, or a grading position.
You may want to use LaTeX to typeset your homework solutions. LaTeX is the standard document preparation system used in the mathematical sciences. Using LaTeX makes it easier for you to revise and edit your solutions and for us to read them, so you will never lose points for illegibility.
My preferred LaTeX editors are TexShop for Mac and TexStudio for Windows. If you would like to give LaTeX a try on the web without installing anything on your computer, Overleaf is a good option.
Not so short intro to LaTeX. A LaTeX tutorial.
Homework template files: tex, cls, jpg, pdf.
Test 1: 12%, Test 2: 12%, Final: 18%
In an effort to make tests less time-consuming and less stressful, we are going to experiment with dividing each test into two parts: a traditional in-class portion, and a take-home portion. Two tests will be given during the semester and one will be given at our regularly scheduled final exam period.
The two 70-minute in-class tests are scheduled for Thursday, Sep. 30 and Thursday, Nov. 4. Each midterm will cover roughly one-third of the course content. A comprehensive in-class final will be held during the normal two-hour exam slot. Please wait until the official University final exam schedule is finalized before making your end-of-semester travel plans.
You may bring one double-sided 8.5" x 11" sheet of notes to each midterm test and two such sheets to the final. Note sheets may be either handwritten or typeset. You may not use any other aids during the exam, including but not limited to books, lecture notes, calculators, phones, or laptops.
The take-home portion of each test will be due on the Tuesday following the in-class portion, in line with the regular homework schedule. You will have at least one week to complete this portion. You are free to consult our course materials for these portions of the tests, but unlike homework assignments, they are to be completed individually.
Class Participation (13%)
Your active participation in class and in discussion sections is an essential part of your learning. Your participation grade will be determined by responses to in-class polls (adminstered through Google Forms), completed discussion worksheets, and other brief activities such as Homework 0. It will also be possible to increase your participation score by thoughtfully asking and answering questions in lectures, in discussions, on Piazza, or during office hours.
All Boston University students are expected to maintain high standards of academic honesty and integrity. It is your responsibility to be familiar with the Academic Conduct Code, which describes the ethical standards to which BU students are expected to adhere and students’ rights and responsibilities as members of BU’s learning community. All instances of cheating, plagiarism, and other forms of academic misconduct will be addressed in accordance with this policy. Penalties for academic misconduct can range from failing an assignment or course to suspension or expulsion from the university.
If you find a mistake in the grading, Gradescope has a feature built in for requesting regrades. We will accept regrade requests for up to one week after each homework assignment or test is returned. Before submitting a regrade request, please make sure you have read and understood the distributed solutions. Regrade requests must point out specific factual errors
in how the grader interpreted your solution. To ensure grading consistency, we cannot accommodate requests based on disagreements about how much a given mistake should correspond to a point value.
Students are expected to attend each class session unless they have a valid reason for being absent. If you must miss class due to illness or another reason, please notify the instructor as soon as possible, ideally before the absence.
Absence Due to Religious Observance
If you must miss class due to religious observance, you will not be penalized for that absence and you will receive a reasonable opportunity to make up any work or examinations that you may miss. Please notify the instructor of absences for religious observance as soon as possible, ideally before the absence.
In the event of the death of an immediate family member, you should notify your advisor, who will help you coordinate your leave. You will be automatically granted five weekdays of leave, and if necessary, you advisor will help you to petition the Dean for additional leave time. You may also request a leave of absence due to bereavement. Please contact your advisor, who will help you with the process.
Students with documented disabilities, including learning disabilities, may be entitled to accommodations intended to ensure that they have integrated and equal access to the academic, social, cultural, and recreational programs the university offers. Accommodations may include, but are not limited to, additional time on tests, staggered homework assignments, note-taking assistance. If you believe you should receive accommodations, please contact the Office of Disability Services to discuss your situation. This office can give you a letter that you can share with instructors of your classes outlining the accommodations you should receive. The letter will not contain any information about the reason for the accommodations.
If you already have a letter of accommodation, you are encouraged to share it with your instructor as soon as possible.
Disability & Access Services
25 Buick Street, Suite 300
If you feel that you have received an arbitrary grade in a course, you should attempt to meet with the grader before filing a formal appeal. If the student and the instructor are unable to arrive at a mutually agreeable solution, the student may file a formal appeal with the chair. This process must begin within six weeks of the grade posting. To understand how an “arbitrary grade” is defined, please explore the following link.
An incomplete grade (I) is used only when the student has conferred with the instructor prior to the submission of grades and offered acceptable reasons for the incomplete work. If you wish to take an incomplete in this class, please contact the instructor as soon as possible but certainly before the submission of final grades. To receive an incomplete, you and your instructor must both sign an “Incomplete Grade Report” specifying the terms under which you will complete the class.
Student Health Services
Offers an array of health services to students, including wellness education and mental health services (behavioral medicine).
Medical Leave of Absence
If you must take a leave of absence for medical reasons and are seeking to re-enroll, documentation must be provided to Student Health Services so that you may re-enroll. To take a medical leave, please talk with SHS and your advisor, so that they may assist you in taking the best course of action for a successful return.
The International Students & Scholars Office is committed to helping international students integrate into the Boston University community, as well as answering and questions and facilitating any inquiries about documentation and visas.