COURSE DIRECTOR	CLASSES (see also Lecture Schedule Information)
G. Tourlakis	Tuesday and Thursday
Room 2051, CSB	11:30  - 13:00
Telephone: 736-2100-1-66674	Classroom: CCB 120
e-mail: gt@cs.yorku.ca	York Campus

We will initially study some advanced topics in Automata and Language theory that build on your previous
knowledge (obtained in COSC 2001). For example, we may look at the Myhil-Nerode theorem for automata,
extensions of the pumping Lemma for CFL, Parikh's theorem.

Our main aim, however, will be a thorough study of Computability and an introduction to Complexity.
Topics will be chosen from Turing computability and Kleene computability. Church's Thesis.
Primitive recursion and Loop Programs, Unsolvability and reductions,
Godel's incompleteness theorem through the halting problem.
Blum's axioms for complexity. "Feasible" and "Unfeasible" computations: P, NP, and NP-complete problems.
Cook's theorem. More reductions.

Prerequisites. General Prerequisites, including COSC 3101 3.0.

The essential prerequisite for COSC 4111/5111 is a certain degree of proficiency in following and formulating combinatorial arguments. Such proficiency should be normally acquired by a student who has successfully
completed a course such as COSC 2001.03 (or COSC 3101.03) and MATH 1090.03 / MATH 2090.03.
Students who have not completed any of the above courses, but (strongly) believe nevertheless that they have
the equivalent background, should seek special permission to enroll in consultation with the instructor.

Work-Load and Grading.

The course grade will be based mainly on about 3-4 homework assignments that will be completed
by students individually . There will be no programming problems, but each assignment
will consist of a number of theoretical problems, for example "prove that such-and-such
function is not computable", or "prove that such-and-such function is primitive recursive", etc.

Textbooks.

• D. C. Kozen, Automata and Computability, Springer-Verlag, 1997.

• G. Tourlakis, Computability , Reston Publishing Company, 1984.

References.

(1) J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation,
Addison-Wesley.

For more on Primitive Recursive and (total) Recursive functions see:

(2) R. Péter, Recursive Functions , Academic Press (Number-theoretic approach, rigorous, fairly difficult).

For more on unsolvability of concrete problems of combinatorial or number theoretical nature, see:

(3) M. Davis, Computability and Unsolvability , McGraw-Hill (Turing approach, rigorous, fairly difficult).

Matijasevic’s proof of the unsolvability of Hilbert’s 10th problem, using methods initiated by Davis
in (3) can be found in:

(4) Y.I. Manin, A Course in Mathematical Logic, Springer-Verlag (quite difficult).

For more on recursion theory, in general, see:

(5) H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill (Semi-formal
using Church’s thesis throughout; difficult).

Finally, for more on machines (at an elementary level), see:

(6) M. Minsky, Computation; Finite and Infinite Machines, Prentice-Hall. __