Complexity Theory

Lecturer: Prof. Dr. Heribert Vollmer

Frequency: every two years (odd years) in the winter semester

Type of course: lecture and exercise (2 lectures + 1 exercise + 2 seminars, 7 ECTS)

Exam: oral exam

This module imparts advanced knowledge about concepts, techniques, and phenomena of complexity theory. After successful completion, students are able to analyze algorithmic problems with respect to various complexity aspects. They assess the consequences of completeness results and develop complexity classifications for new algorithmic problems.

Outline:

• The polynomial-time hierarchy
• Probabilistic complexity classes
• Counting classes
• Toda’s theorem
• Isomorphism of complete sets (Berman-Hartmanis conjecture)
• Sparse complete sets and advice classes (Karp-Lipton theorem)
• Relativization (Baker-Gill-Solovay theorem)
• Interactive proof systems

The final examination of the module is an oral exam.

Schedule

The exam dates are assigned via an internal institute website (see link below). Note: This does not replace registration for the exam in QIS.

Registration

Depending on your examination regulations, registration in QIS may be required (see link below).

Coursework Requirement

If your examination regulations require coursework for this module, please contact the lecturer.