Computability Theory

Dr. Heinrich Rolletschek

September 7, 2015

0.1 Time and place:

Thursday, 8:30–10:00, T 406/1, beginning October 8 2015.

0.2 About the course:

In contrast to courses like Design and Analysis of Algorithms, where specific algorithms are sought for specific problems, this course deals with the very notion of (algorithmic) computability. The notion of partial recursive function is introduced as a mathematically precise equivalent for the informal notion of algorithmically computable partial function, and mathematical properties of partial recursive functions are investigated. In particular, this allows to derive negative results: certain mathematical problems cannot be solved algorithmically even in principle. Some considerations in computability theory also concern the old question whether or not computers may completely replace humans (as mathematical problem solvers).

One natural sequel is the subject of abstract complexity, one of the topics in the follow-up course Decidability- and Complexity Classes.

0.3 Contents:

Chapters 1–6 deal with the following issues:

0.4 Literature:

Lecture notes will be handed out. Among textbooks we mention

0.5 Exam:

Oral exam by agreement. Just consult me when you are ready.