CS584 Theory of Computation/Complexity Theory

Tue/Thr 12-1:15pm Wilmeth Active Learning Center 3132

Instructor

Elena Grigorescu, elena-g purdue.edu

Office Hours: Tue 1:30-2:30 on Zoom

TA: Maoyuan Raymond Song song683 purdue.edu

Office Hours: Wed 1:30-2:30pm on Zoom.
Announcements

Welcome to CS 584!


Our main class website is on Brighspace

Texts
  • Introduction to the Theory of Computation (3rd edition) by Michael Sipser, Cengage Learning.
  • Recommended: Computational Complexity: A Modern Approach, by Sanjeev Arora and Boaz Barak, Cambridge University Press. Earlier draft Theory of computation by Dexter Cozen, Springer.
Course description
This is an introductory, graduate-level course on the theory of computation. We will focus on the fundamental mathematical model of a Turing Machine, discuss its powers and limitations, discuss computational resources that a TM might use (time, space, randomness) and the complexity classes associated with them (P, NP, PSPACE, BPP, RP, etc). In the second part of the course we'll cover more advanced topics, possibly including Interactive Proofs (IP, PCP).
Grading
  • 20% for homeworks (expect bi-weekly)
  • 30% for the midterm
  • 35% for the final
  • 10% for project
  • 5% for class participation/quizzes (including LaTeX solutions for requested hw problems--to be shared with the class)
Schedule (tentative)
  • Aug 24 1. Intro. Turing machines variants. HW0
  • Aug 26 2. Decidability. Undecidability.
  • Aug 31 3. Diagonalization
  • Sep 2 4. Reducibility
  • Sep 4 5. Computation history method
  • Sep 9 6. Recursion theorem
  • Sep 11 7. Time Complexity. P
  • Sep 16 8. NP
  • Sep 21 9. NP completeness
  • Sep. 23 10. Cook-Levin's theorem
  • Sep. 28 11. Circuit complexity
  • Sep 30 12. MIDTERM (in class)
  • Oct 5 14. Space complexity
  • Oct 7 15.PSPACE, TQBF, Savitch's theorem
  • Oct 12 October break.
  • Oct 14 16. PSPACE games
  • Oct 19 17. L, NL, coNL
  • Oct 21 18. NL=coNL
  • Oct 26 19. Hierarchy theorems
  • Oct. 28 20. Oracles. Limits to diagonalization
  • Nov 2 21. TMs with alternation
  • Nov 4 22 Probabilistic computation. Markov, Chebyshev, Chernoff inequalities.
  • Nov. 9 23 Primality testing
  • Nov. 11 24 Polynomial identity testing. Schwarz-Zippel lemma. Deciding perfect matching in bipartite graphs.
  • Nov. 16 25 Branching programs. Interactive Proofs. ZKP. Arithmetization.
  • Nov. 18 26. #SAT in IP. IP=PSPACE
  • Nov 23 27 Probabilistically Checkable Proofs
  • Nov. 25 28 Thanksgiving break
  • Nov. 30 28 Quantum computing basics
  • Dec 2 28 Review
  • Dec 7 28 Projects
  • Dec. 9 29 Projects
  • Dec 13 31. Final exam 1-3pm WALC B074
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