CSC 363: Lectures

Week	Date	Topics	Readings	Tutorial	Notes
1	May 16	Course Introduction Computability and Turing machines	Section 3.1 (review chapters 0, 1, 2 as needed)	exercises	lecture notes
2	May 23	Other models of computation	Sections 3.2, 3.3	exercises	lecture notes Additional example of TM description
3	May 30	Church-Turing Thesis, Decidability and recognizability	Section 4.1	exercises	lecture notes
4	June 6	Diagonalization, the Halting problem	Section 4.2	exercises	lecture notes
5	June 13	Reducibility	Section 5.1	exercises	lecture notes
6	June 20	Term test 1 Mapping reducibility	Section 5.3, exercise 5.28	no tutorial	lecture notes
7	June 27	Computational Complexity Models of efficient computation	Sections 7.1, 7.2	exercises	lecture notes
8	July 4	Complexity classes P, NP, coNP	Section 7.3	exercises	lecture notes
9	July 11	Polytime reducibility and NP-completeness	Section 7.4	exercises	lecture notes Additional example of ≤_p
10	July 18	NP-completeness	Section 7.5	exercises	lecture notes
11	July 25	Term test 2 Self-reducibility	Section 8.1	no tutorial	lecture notes
12	Aug 1	Space complexity	Sections 8.2, 8.3	exercises	lecture notes
13	Aug 8	Other complexity classes Dealing with intractability	Sections 8.4, 8.5, 9.1	past exam (PDF)	lecture notes

All readings are from the course textbook, Michael Sipser, Introduction to the Theory of Computation, 2nd edition.

Many of the lecture notes included here are adapted from Francois Pitt's CSC 363 notes.

Course outline

Lecture/tutorial topics

The following topics will be covered in this course, in the order listed. For each topic, we have indicated the approximate number of weeks required to cover that topic as well as a list of the relevant sections in the textbook.

Computability Theory [6 weeks]
(Chapters 3, 4, 5 in the textbook)
- Turing machines: definitions and examples (section 3.1)
- Other models of computation, the Church-Turing thesis (sections 3.2, 3.3)
- Diagonalization, the Halting problem (sections 4.1, 4.2)
- Decidability and recognizability, examples (sections 4.2, 5.1)
- Reducibility, examples (sections 5.1, 5.2)
- Mapping reducibility, examples (section 5.3)
Complexity Theory [7 weeks]
(Chapters 7, 8, 10 in the textbook)
- Models of efficient computation (sections 7.1, 7.2)
- P, NP, coNP, examples (section 7.2, 7.3)
- Polytime reducibility, NP-completeness (section 7.4)
- Cook's theorem, more NP-completeness (section 7.5)
- Self-reducibility (not in textbook)
- Space complexity and other complexity classes (sections 8.1, 8.2, 8.3, 9.1)

Learning objectives

By the end of this course, students should

be familiar with fundamental restrictions on computability:
- be familiar with Turing machines;
- understand the notions of decidability and semi-decidability;
- know that the Halting problem is undecidable;
- understand and be able to apply techniques for showing undecidability (diagonalization, reductions);
understand the importance of computational complexity:
- be familiar with the definitions of P and NP;
- be able to demonstrate membership in P or NP;
- be familiar with the definition of NP-completeness;
- be able to apply techniques for showing NP-completeness;
- know other standard complexity classes (PSPACE, EXP).