Advanced topics in theoretical computer science
Slides
27.10.2021:
Organization
[organization.pdf]
Introduction
[introduction.pdf]
Audio Commented Slides
(Online: 27.10.2021)
3.11.2021: Turing Machines and Computability (Part 1)
[recap-tm.pdf]
Audio Commented Slides
(Online: 2.11.2021)
10.11.2021: Turing Machines and Computability (Part 2)
[recap-tm2.pdf]
(
Updated version: 16.11.2021
)
10.11.2021: Register Machines (Part 1)
[register-machines1.pdf]
Audio Commented Slides
(Online: 10.11.2021)
17.11.2021: Register Machines (Part 2)
[register-machines2.pdf]
Slides about structural induction:
[structural-induction.pdf]
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(Online: 16.11.2021)
24.11.2021: Register Machines (Part 3)
[register-machines3.pdf]
24.11.2021: Register Machines: Wrapping up
[register-machines-recap.pdf]
Proof: The class of all unary loop computable functions is r.e.
[class-of-unary-loop-comp-functions-is-re.pdf]
Audio Commented Slides
(Online: 23.11.2021)
1.12.2021: Recursive functions (Part 1)
[recursive-functions1.pdf]
Audio Commented Slides
(Online: 30.11.2021)
8.12.2021: Recursive functions (Part 2)
[recursive-functions2.pdf]
Audio Commented Slides
(Online: 8.12.2021)
15.12.2021: Recursive functions (Part 3)
[recursive-functions3.pdf]
Examples simultaneous recursion
[pdf]
Audio Commented Slides
(Online: 15.12.2021)
22.12.2021: Recursive functions (Part 4)
[recursive-functions4.pdf]
[example2-f-is-mu-g-15-06-2021.pdf]
(added on 20.12.2021)
Audio Commented Slides
(Online: 20.12.2021)
05.01.2022: Computability and (Un-)Decidability, Part I
[computability1.pdf]
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(Online: 05.01.2022)
12.01.2022 and 19.01.2022 Computability and (Un-)Decidability, Part II
[computability2.pdf]
12.01.2022: pages 1-29
Audio Commented Slides
(Online: 12.01.2022 (PCP - Parts 1-6))
19.01.2022: pages 30-38
Audio Commented Slides
(Online: 19.01.2022 (PCP - Part 7 + Applications Parts 1-5))
19.01.2022: Complexity, Part I
[complexity1.pdf]
Audio Commented Slides
(Online: 19.01.22 (Complexity - Introduction and Parts 1-3))
26.01.2022: Complexity, Part II
[complexity2.pdf]
(Online: 26.01.2022)
Important for the exam: pages 1-69
Audio-Commented Slides for this part
(Online: 26.01.2022)
Additional information
, not important for the exam
Proofs NP-completeness colorability (external links)
Coloring is NP-complete: Proof
[coloring-np-complete-proof.pdf]
3-colorability is NP-complete: Proof
[External Link]
Not important for the exam
2.02.2022: Additional informations: complexity, computability
Complexity, Part III
[complexity3.pdf]
The structure of PSPACE (some explanations)
Other direction in complexity theory
Other models for computability
[other-models-of-computability.pdf]
(Online: 2.02.2022)
Audio-Commented Slides for this part
(Complexity: Parts 1 and 2; Computability: Part 3)
(Online: 2.02.2022)
9.02.2022: Overview: List of topics
[summary.pdf]
Audio-Commented Slides
(Online: 9.02.2022)