YORK UNIVERSITY
Department of Computer Science
COSC4111/5111—Automata and Computability
Course Outline-Fall 2004
First day of class: September 9, 2004
COURSE DIRECTOR | CLASSES (see also Lecture Schedule ) |
G. Tourlakis | Tuesday and Thursday |
Room 2051, CSEB | 13 :00 - 14:30 |
Telephone: 736-2100-1-66674 | Classroom: PSE 321 |
e-mail: gt@cs.yorku.ca | York Campus |
It is the responsibility of students to check the course web page weekly for course related information.
Our main aim 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 via Diagonalisation and Reductions.
The connection between
uncomputability and unprovability: Gödel'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 and, by transitivity, MATH1090 3.0 and
MATH(COSC)1019 3.0 or
similar courses (MATH2320 or MATH2090).
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.
Students who have not completed
any of the above courses, but who (strongly) believe
nevertheless that they have
the equivalent background,
should seek special permission to enrol 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.
Graduate students in the course
(registered in COSC5111) will be assigned additional homework and
readings,
expected to probe the material further.
Textbook.
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. __