18.404/6.5400 Fall 2025
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, proof-oriented 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.

Information, Problem Sets, and Study Materials

Homework submission instructions. Upload a single file with all non-optional problems to Gradescope 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, otherwise the grader might not find your submission. 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. At noon on the due date, the regular Gradescope assignment for non-optional problems will close and a new "late submission" assignment will appear. 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. Upload only those non-optional 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 and will be subject to the late penalty. 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. Optional problem parts may not be submitted separately for lateness consideration.

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.

Resources

Course Staff

Office Hours (starting Tuesday 9/9)

Friday Recitation Times and TAs

Recitation Dates and Notes

  1. September 5 - Leo's notes
  2. September 12 - Jonathan's notes
    September 19 - No classes (student holiday)
  3. September 26
  4. October 3
  5. October 10
  6. October 17
  7. October 24
  8. October 31
  9. November 7
  10. November 14
  11. November 21
  12. December 5
Notes are generally posted by the Tuesday following the Friday recitation.

Lecture Schedule

  1. 9/4  Introduction, finite automata, regular expressions §1.1
  2. 9/9  Nondeterminism, closure properties, Reg Exprs → FA §1.2-1.3
  3. 9/11  Reg Exprs ← FA, Proving non-regularity via pumping lemma, CFGs §1.4-2.1
  4. 9/16  Context free languages, Pushdown Automata, CFG ⇆ PDA §2.2
  5. 9/18  Context-free pumping lemma, Turing machines §2.3,3.1 Pset 1 DUE (noon)
  6. 9/23  TM variants, Church-Turing thesis §3.2-3.3
  7. 9/25  Decision problems for automata and grammars §4.1
  8. 9/30  Undecidability §4.2
  9. 10/2  Reducibility §5.1,5.3 Pset 2 DUE (noon)
  10. 10/7  Computation history method §5.2
  11. 10/9  Recursion theorem, Logic §6.1-6.2
  12. 10/14  Time complexity §7.1 Pset 3 DUE (noon)
  13. 10/16  Midterm Exam (during regular lecture time, Walker)
  14. 10/21  P and NP, SAT, Poly-time reducibility §7.2-7.3
  15. 10/23  NP-completeness §7.5
  16. 10/28  Cook-Levin theorem §7.4
  17. 10/30  Space complexity, PSPACE §8.1-8.2
  18. 11/4  Savitch's theorem, PSPACE-completeness §8.3
  19. 11/6  Games, Generalized geography, L and NL §8.3-8.4 Pset 4 DUE (noon)
    11/11  NO CLASS --- Veterans Day
  20. 11/13  NL-completeness, NL = coNL §8.4
  21. 11/18  Hierarchy theorems §9.1
  22. 11/20  Provably intractable problems, oracles §9.2 Pset 5 DUE (noon)
  23. 11/25  Probabilistic computation, BPP §10.2
    11/27  NO CLASS --- Thanksgiving
  24. 12/2  An interesting language in BPP, Arithmetization §10.2
  25. 12/4  Interactive proof systems, IP §10.4 Pset 6 DUE (noon)
  26. 12/9  coNP ⊆ IP §10.4

Exam Schedule

Exams are closed book. No book, notes, or laptop. A crib sheat will be allowed.

Student Support

For serious urgent matters at any time, every student may contact the 24x7 Dean on Call at (617) 253-1212.

2020 Lectures

Accessibility