18.404/6.5400 Fall 2024
Introduction to the Theory of Computation
Required background. To succeed in this course, you need experience and skill with mathematical concepts, theorems, and proofs. If you did reasonably well in 18.062, 18.200, or any other substantial, prooforiented mathematics subject, you should be fine. The course moves quickly, covering about 90% of the textbook. The problem sets generally require proving some statement, and creativity in finding proofs will be necessary.
Homework submission instructions.
Upload a single file with all nonoptional problems to
Gradescope
(will be set up by Thursday 9/12) by the due date.
Handwritten is ok as long as we can read it easily,
otherwise use latex.
When Gradescope prompts you, mark the pages containing each problem.
If you upload several files, the last upload file replaces all previous
files, so upload the complete set.
Do not upload individual problems separately.
Late homework submission.
You may submit any individual problems after the due date, before 11:59pm
the following day, for a 1 point per problem late penalty deduction.
In each pset, you may submit some problems or problem parts on time
and others late. (The penalty will be 10% of the part's point value.)
At Noon on the due date, the regular Gradescope assignment
for nonoptional problems will close
and a new "late submission" assignment will appear.
Upload only those nonoptional problems you wish
to be counted as late, together in a single file.
You may resubmit problems you submitted previously if you wish to change
your answer, but these will be marked late and get the 1 point penalty.
DO NOT RESUBMIT UNCHANGED PROBLEMS you submitted previously.
The late submissions (even if unmarked) will override earlier submissions.
Note: We cannot accept unexcused (see
"Student Support" below) homework after the late submission deadline.
Optional problem submission. Submit the optional problems
to a separate "optional problem" assignment. That assignment is
configured to accept both ontime and late submissions. You will
receive the usual 1 point penalty for a late optional problem.
Regrade requests. If you feel that your work was incorrectly
graded, you may submit a regrade request through Gradescope. Please
review your graded papers promptly; regrade requests are accepted
only for two weeks from the original pset due date. Please do not abuse
the regrade system by making lots of frivolous requests; we have limited
grader capacity.
If you need to communicate with us about the psets
(e.g., medical extensions),
email the grading team.
 Lecturer:
Michael Sipser, sipser@mit.edu
 Head TA, Grading Coordinator: Freya Edholm, fe2o3@mit.edu
 Recitation TA: Sarah Bentley, sbentley@mit.edu
 Grading Coordinator TA: Axel Adjei, asadjei@mit.edu
 Recitation TA: Sean Cheng, scheng12@mit.edu
 Recitation TA: Leo Gagnon, leognon@mit.edu
 Recitation TA: Jonathan Huang, jhuang25@mit.edu
 Recitation TA: Zed Li, zli11010@mit.edu
 Grading Coordinator TA: Jakin Ng, jakinng@mit.edu
 Grading Coordinator TA: Jon Rosario, jonros@mit.edu
 Recitation TA: Nathan Sheffield, shefna@mit.edu
 Recitation TA: Leo Yao, leoy@mit.edu
 Recitation TA: Anna Zhang, azhang03@mit.edu
 Recitation TA: Zimi Zhang, zimi@mit.edu
 TA office hours start Wednesday 9/11
 Sundays, 24pm, 2151, Leo G
 Mondays 1011am, 2139, Jonathan and Zimi
 Mondays 11amnoon, 2136, Nathan
 Mondays 23pm, 26168, Zed and Leo Y
 Mondays 34pm, 26168, Leo Y
 Monday 56pm,
Zoom
(MIT Certificate required), Mike
 Tuesdays 4:155pm, 2438 (or down the hall), Mike
 Tuesdays 5:307:30pm, 2103, Anna
 Wednesdays 1011am, 2136, Jonathan and Zimi
 Wednesdays 11amnoon, 2136, Nathan
 Wednesdays 23pm, 133101, Zed
 Wednesdays 34pm, 133101, Sarah and Freya
 Wednesdays 45pm, 26322, Sarah and Sean
 Wednesdays 56pm, 26322, Sean
Lectures are held in room 54100 on Tuesdays and Thursdays from 2:30 to 4pm.
The onehour recitations meet Fridays at the following times and rooms:
 10:00am, 4159, Sarah
 11:00am, 4159, Anna
 12:00pm, 4257, Jonathan and Zimi
 1:00pm, 4257, Nathan and Leo Y
 2:00pm, 4145, Zed
 3:00pm, 4145, Sean and Leo G
Notes are generally posted by the Tuesday following the Friday recitation.
 September 6
 Anna's notes

9/5 Introduction, finite automata, regular expressions §1.1

9/10 Nondeterminism, closure properties, Reg Exprs → FA §1.21.3

9/12 Reg Exprs ← FA, Proving nonregularity via pumping lemma, CFGs §1.42.1

9/17 Context free languages, Pushdown Automata, CFG ⇆ PDA §2.2

9/19 Contextfree pumping lemma, Turing machines §2.3,3.1 Pset 1 DUE (noon)

9/24 TM variants, ChurchTuring thesis §3.23.3

9/26 Decision problems for automata and grammars §4.1

10/1 Undecidability §4.2

10/3 Reducibility §5.1,5.3 Pset 2 DUE (noon)

10/8 Computation history method §5.2

10/10 Recursion theorem, Logic §6.16.2
10/15 NO CLASS  Student Holiday

10/17 Time complexity §7.1 Pset 3 DUE (noon)

10/22 P and NP, SAT, Polytime reducibility §7.27.3

10/24 Midterm Exam (during regular lecture time, in Walker)

10/29 NPcompleteness §7.5

10/31 CookLevin theorem §7.4

11/5 Space complexity, PSPACE §8.18.2

11/7 Savitch's theorem, PSPACEcompleteness §8.3 Pset 4 DUE (noon)

11/12 Games, Generalized geography, L and NL §8.38.4

11/14 NLcompleteness, NL = coNL §8.4

11/19 Hierarchy theorems §9.1

11/21 Provably intractable problems, oracles §9.2 Pset 5 DUE (noon)

11/26 Probabilistic computation, BPP §10.2
11/28 NO CLASS  Thanksgiving

12/3 An interesting language in BPP, Arithmetization §10.2

12/5 Interactive proof systems, IP §10.4 Pset 6 DUE (noon 12/6)

12/10 coNP ⊆ IP §10.4
Midterm exam: Thursday, October 24, 2:30  4pm,
Walker (Building 50),
top floor.
Final exam: During finals week. Time and location announced in the third week of the term.
If you are dealing with a personal or medical issue that
may affect your participation in any MIT class, please discuss it with
Student Support Services (S3)
at 6172534861.
Graduate students may contact
GradSupport.
We cannot excuse you from coursework without support from S3 or
GradSupport.
For serious urgent matters at any time, every student
may contact the 24x7 Dean on Call at (617) 2531212.
If you may require disability accommodations,
please speak early in the semester with
Associate Dean Kathleen Monagle then let me know so that we can
work together to get your accommodation logistics in place.
Accessibility