This course introduces some classical models of computation, and it covers the fundamental notions, techniques, and results of computability theory.
Times and location
Class: Wednesday, 12-14. Ludwigstr. 31, Room 021.
Exercise session: Thursday, 14-15. Ludwigstr. 28, Room 503.
Basic knowledge of first-order logic.
Final exam on 24-07
N. J. Cutland, Computability: an introduction to recursive function theory.
Course program (preliminary)
Part I: models of computation
08-05 Unlimited register machines
Material: Ch. 1.4-1.5.
Exercises for 16-05.
15-05 Recursive functions
Material: Ch. 2 and 3.2.
Exercises for 23-05.
22-05 Turing machines
29-05 Post systems
05-06 The Church-Turing thesis, coding of programs
Part II: introduction to recursion theory
12-06 Diagonalization, halting problem, s-m-n theorem, Kleene normal form
19-06 Universal program, Reduction between problems, Rice’s theorem
26-06 Partial decidability
03-07 Recursive and recursively enumerable sets
10-07 An application: Church’s theorem
17-07 Connections with arithmetics and Gödel’s theorem
24-07 Final exam