18.404/6.5400 Fall 2023
Introduction to the Theory of Computation
Required background. To succeed in this class, 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, proof-oriented mathematics class, you should be fine. The class moves quickly, covering about 90% of the textbook. The homework assignments generally require proving some statement, and creativity in finding proofs will be necessary.
** Access requires MIT certificates.
Homework submission instructions.
Upload a single file with all non-optional problems to
Gradescope (will be set up by Thursday 9/14)
before 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 overrides all previous
uploads, so do not upload individual problems separately.
Late homework submission.
You may submit any individual non-optional 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 will close
and a new "late submission" assignment will appear. Please upload only
those problems you wish to be counted as late. 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 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 on-time 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 Grading Coordinator TA: Freya Edholm, fe2o3@mit.edu
- Head Recitation TA: Jett Wang, jett@mit.edu
- Recitation TA: Fatima Abbasi, fabbasi@mit.edu
- Recitation TA: Vaishnavi Addala, vaddala9@mit.edu
- Recitation TA: Sean Cheng, scheng12@mit.edu
- Grading Coordinator TA: Della Hendrickson, della@mit.edu
- Recitation TA: Jonathan Huang, jhuang25@mit.edu
- Recitation TA: Mark Jabbour, mjabbour@mit.edu
- Grading Coordinator TA: Jeffery Li, jeli@mit.edu
- Recitation TA: Samuel Tenka, samtenka@mit.edu
- Recitation TA: Audrey Xie, ahx@mit.edu
- Recitation TA: Yuxuan Zheng, yuxuanz@mit.edu
- Mondays 2-3pm, 2-361, Yuxuan
- Mondays 3-4pm, 2-361, Fatima and Yuxuan
- Mondays 4-5pm, 4-153, Audrey and Fatima
- Mondays 5-6pm,
Zoom
(MIT Certificate required), Mike
- Tuesdays 4:15-5pm, 2-438 (or down the hall), Mike
- Tuesdays 7-9pm, 26-204, Vaishnavi and Jett
- Wednesdays 11-noon, 8-205, Jonathan and Jeffery [Except Nov 15 in 4-163]
- Wednesdays 4-5pm, 26-204, Audrey and Mark
- Wednesdays 5-6pm, 26-204, Jonathan and Mark
- Wednesdays 6-7pm, 2-135, Freya and Sam
- Wednesdays 7-8pm, 2-135, Sean and Sam
- Wednesdays 8-9pm, 2-135, Sean and Jett
Weeks when problem sets are due will be staffed by two TAs during office
hours;
other weeks will be staffed by one TA.
Lectures are held in room 34-101 on Tuesdays and Thursdays from 2:30 to 4pm.
The one-hour recitations meet Fridays at the following times and rooms:
- 10:00am, 4-261, Vaishnavi and Jonathan
- 11:00am, 4-261, Mark
- 12:00pm, 4-257, Jett
- 1:00pm, 4-257, Fatima and Yuxuan
- 2:00pm, 4-145, Sean and Audrey
- 3:00pm, 4-145, Sam
Notes are generally posted by the Monday following the Friday recitation.
- September 8
- Jett's notes
- September 15
- Sean's notes
- September 22
- No classes (student holiday)
- September 29
- Mark's notes
- October 6
- Jonathan's notes
- October 13
- Mark's notes
- October 20
- Fatima's notes
- October 27
- Yuxuan's notes
- November 3
- Vaishnavi's notes
- November 10
- No classes (Veterans Day)
- November 17
- Audrey's notes
Midterm exam: Thursday, October 26, 2:30 - 4pm,
Walker (Building 50),
top floor.
Final exam: Friday, December 22, 9am - Noon,
DuPont Gym.
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 617-253-4861. They have a Dean on Call 24x7 at 617-253-1212.
Graduate students may contact
GradSupport.
We cannot excuse you from coursework without support from S3 or
GradSupport.
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.
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9/7 Introduction, finite automata, regular expressions §1.1
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9/12 Nondeterminism, closure properties, Reg Exprs → FA §1.2-1.3
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9/14 Reg Exprs ← FA, Proving non-regularity via pumping lemma, CFGs §1.4-2.1
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9/19 Context free languages, Pushdown Automata, CFG ⇆ PDA §2.2
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9/21 Context-free pumping lemma, Turing machines §2.3,3.1 Pset 1 DUE (noon)
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9/26 TM variants, Church-Turing thesis §3.2-3.3
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9/28 Decision problems for automata and grammars §4.1
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10/3 Undecidability §4.2
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10/5 Reducibility §5.1,5.3 Pset 2 DUE (noon)
10/10 NO CLASS --- Student Holiday
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10/12 Computation history method §5.2
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10/17 Recursion theorem, Logic §6.1-6.2
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10/19 Time complexity §7.1 Pset 3 DUE (noon)
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10/24 P and NP, SAT, Poly-time reducibility §7.2-7.3
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10/26 Midterm Exam
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10/31 NP-completeness §7.5
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11/2 Cook-Levin theorem §7.4
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11/7 Space complexity, PSPACE §8.1-8.2
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11/9 Savitch's theorem, PSPACE-completeness §8.3 Pset 4 DUE (noon)
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11/14 Games, Generalized geography, L and NL §8.3-8.4
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11/16 NL-completeness, NL = coNL §8.4
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11/21 Hierarchy theorems §9.1
11/23 NO CLASS --- Thanksgiving
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11/28 Provably intractable problems, oracles §9.2 Pset 5 DUE (noon)
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11/30 Probabilistic computation, BPP §10.2
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12/5 An interesting language in BPP, Arithmetization §10.2
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12/7 Interactive proof systems, IP §10.4 Pset 6 DUE (noon)
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12/12 coNP ⊆ IP §10.4
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