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Computability and Complexity Theory

Module name (EN):
Name of module in study programme. It should be precise and clear.
Computability and Complexity Theory
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
Applied Informatics, Master, ASPO 01.10.2017
Module code: PIM-BK
SAP-Submodule-No.:
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
P221-0048
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
4V (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
6
Semester: 1
Mandatory course: yes
Language of instruction:
German
Assessment:
Oral examination

[updated 20.12.2017]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

DFI-BK (P610-0278) Computer Science, Master, ASPO 01.10.2018 , semester 1, mandatory course
KIM-BK (P222-0047) Computer Science and Communication Systems, Master, ASPO 01.10.2017 , semester 1, mandatory course
PIM-BK (P221-0048) Applied Informatics, Master, ASPO 01.10.2011 , semester 1, mandatory course
PIM-BK (P221-0048) Applied Informatics, Master, ASPO 01.10.2017 , semester 1, mandatory course
Workload:
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 180 hours (equivalent to 6 ECTS credits).
There are therefore 135 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
None.
Recommended as prerequisite for:
PIM-STI Theoretical Informatics Seminar


[updated 10.10.2023]
Module coordinator:
Prof. Dr. Maximilian Altmeyer
Lecturer:
Prof. Dr. Maximilian Altmeyer


[updated 10.10.2023]
Learning outcomes:
The students will be able to define the most important concepts from the computability and complexity theory and explain them using examples. They can understand the basic mathematical properties of hardware and software and are able to identify and apply theoretical concepts that solve practical problems. Students can explain the principal limitations to which certain problems are subject and analyze new problems with regard to these limitations.
 
The students can determine the complexity of problems regarding runtime and storage space and implement this knowledge to draw conclusions about the practical implementation of algorithms.


[updated 20.12.2017]
Module content:
1   Automata and languages
       * Finite and infinite automata
       * Regular expressions
       * Kleene´s recursion theorem
       * Quotient automaton
2   Computability theory
       * Turing machines
       * Church-Turing thesis
       * Generators
       * Decidability
       * Reduction
3   Complexity theory
       * Time complexity
       * NP-completeness
       * Space complexity
 


[updated 24.02.2018]
Teaching methods/Media:
Lecture, exercises, discussions

[updated 20.12.2017]
Recommended or required reading:
SIPSER Michael: Introduction to the theory of computation, Course Technology, 3rd edition, 2012
SAKAROVITCH Jacques: Elements of Automata Theory, Cambridge University Press, 2009
 


[updated 20.12.2017]
Module offered in:
WS 2024/25, WS 2023/24, WS 2022/23, WS 2021/22, WS 2020/21, ... 
[Tue Dec  3 18:40:31 CET 2024, CKEY=pbk, BKEY=pim2, CID=PIM-BK, LANGUAGE=en, DATE=03.12.2024]