Lecture List

Caveat

These are electronic records of class discussion from Math 304 (Theory of Computability). They are generally captured as a class unfolds, and slightly cleaned up afterwards. They are not clean, carefully-planned lecture notes in the usual sense. They are more an electronic equivalent of notes on the blackboard: they record some of what the instructor said, some of what students said, the things that really happened in the class—including the misunderstandings, false starts, and similar things that happen in real classes. The goal of these notes is as much to help students remember how they learned as it is to help them remember what they learned (because the “how” of learning is at least as important as the “what”).

Please make WWW or other electronic links to this page only—I want people reading these notes to see the “caveat” above.

Send comments, questions, etc. related to these notes to Doug Baldwin.

1. Jan. 20—Introduction
2. Jan. 22—Finite Automata
3. Jan. 25—Nondeterministic Finite Automata
4. Jan. 27—Equivalence of Nondeterministic and Deterministic Finite Automata
5. Jan. 29—Closure Properties of the Regular Languages
6. Feb. 1—Regular Expressions
7. Feb. 3—Regular Expressions Are Equivalent to Regular Languages
8. Feb. 5—Regular Expressions Are Equivalent to Regular Languages, Part 2
9. Feb. 8—Introduction to the Pumping Lemma
10. Feb. 10—The Pumping Lemma, Part 2
11. Feb. 12—The Pumping Lemma, Part 3
12. Feb. 15—Class cancelled, no lecture notes
13. Feb. 17—Exam 1, no lecture notes
14. Feb. 19—Context Free Grammars
15. Feb. 22—Pushdown Automata
16. Feb. 24—Every CFG has a PDA
17. Feb. 26—Every PDA has a CFG
18. Feb. 29—The Pumping Lemma for Context Free Languages
19. Mar. 2—Deterministic Context Free Languages
20. Mar. 4—Online Discussion, no notes
21. Mar. 7—Turing Machines
22. Mar. 9—Variations on Turing Machines
23. Mar. 11—The Church-Turing Thesis
24. Mar. 21—Turing-Decidable Problems
25. Mar. 23—Exam 2, no lecture notes
26. Mar. 25—Undecidable Problems
27. Mar. 28—Unrecognizable Problems
28. Mar. 30—Introduction to Reduction Proofs
29. Apr. 1—Reduction Proof Examples
30. Apr. 4—Reduction Proofs and Rice’s Theorem
31. Apr. 6—Reduction and Computation Histories
32. Apr. 8—The Post Correspondence Problem, Part 1
33. Apr. 11—The Post Correspondence Problem, Part 2
34. Apr. 13—Ambiguity of CFGs is Undecidable
35. Apr. 15—Introduction to the Recursion Theorem
36. Apr. 18—The Recursion Theorem via Programs
37. Apr. 20—Applications of the Recursion Theorem
38. Apr. 22—Introduction to Lambda Calculus
39. Apr. 25—Arithmetic in the Lambda Calculus
40. Apr. 27—Logic in the Lambda Calculus
41. Apr. 29—Logic in the Lambda Calculus, Part 2
42. May 2—Recursion in the Lambda Calculus