Complexity Theory 2015/2016
News
- Chapter 22 (Scheduling and Jump Numbers) will not be part of the oral exam !
- Update on Sheet 12. There was a wrong parameter in Exercise 12.2.
- You can find more information on the dates for the oral exams under Exams below.
- Changed order of the exercises on Sheet 8: part d) and c) were swapped.
- Exercise Sheet 7 was updated !
- The tutorials already start this week.
Organisation
Dates and rooms:
- Mondays 15:30 - 17:00 in 46-280
- Wednesdays 13:45 - 15:15 in 46-268
- Tutorials take place on:
- Thursdays 10:00 - 11:30 in 34-420
- Thursdays 17:15 - 18:45 in 34-420.
- Tutorials start in the first week.
- The lecture in KIS and in the Module Handbook.
Exams
There will be an oral exam on the contents of the lecture. To be admitted to the exam, you have to fulfil the following requirements:- 60 percent of your exercises have to be marked by a plus.
- You have to present some of your exercise solutions on the board .
To get a fixed date for your oral exam, please write an e-mail to Peter Chini. Mention your full name, the lecture for which you want to do the exam and your preferred date (11.03 or mid of April) in the e-mail. If you prefer to have your exam in the morning or in the afternoon, you can also mention this.
Don't forget to register the exam with the Prüfungsamt (examination office) as soon as the date is fixed.Lecture Notes
There are handwritten notes on the topics of the lecture:- Lower bounds via crossing sequences. (Week 1)
- Time and Space Complexity Classes. (Week 1/2, preliminary)
- Alphabet reduction, tape reduction, compression, speed-up. (Week 2, preliminary)
- Space vs. time, non-determinism vs. determinism. (Week 3)
- Savitch's theorem. (Week 3)
- Space and time hierarchy results. (Week 3/4)
- Translation theorems. (Week 4)
- Immerman and Szelepcsényi's theorem. (Week 4)
- Summary of the relationship among the robust complexity classes. (Week 4, update)
- L and NL. (Week 5)
- Models of computation for L and NL. (Week 6)
- P and NP. (Week 7)
- PSPACE. (Week 8)
- Alternation. (Week 9)
- Alternation (contd.), the polynomial hierarchy. (Week 9)
- Oracle Turing machines, relativized complexity classes, and a characterization of the polynomial hierarchy. (Week 10)
- Ladner's theorem, diagonalization and its limits. (Week 11)
- Families of Boolean circuits. (Week 12)
- Parallel complexity. (Week 12)
- Non-uniform polynomial time. (Week 13)
- Parameterized complexity. (Week 13)
- Bounded search trees. (Week 13)
- Scheduling and jump number. (Week 14)
- Kernelization. (Week 14)
- Nemhauser and Trotter's theorem. (Week 15)
- Iterative compression. (Week 15)
- Hardness in parameterized complexity. (Week 16)
- Advanced topics in parameterized complexity. (Week 16)
Exercises
Exercises will be made available here on Wednesday evenings. Please hand in your solution in groups of 3 to 4 people in the box in building 34, 4th floor, close to room 401 and the SoftTech AG.- Download Exercise Sheet 1 here.
- Download Exercise Sheet 2 here.
- Download Exercise Sheet 3 here.
- Download Exercise Sheet 4 here.
- Download Exercise Sheet 5 here.
- Download Exercise Sheet 6 here.
- Download Exercise Sheet 7 here.
- Download Exercise Sheet 8 - Christmas Edition here.
- Download Exercise Sheet 9 here.
- Download Exercise Sheet 10 here.
- Download Exercise Sheet 11 here.
- Download Exercise Sheet 12 here.
- Download Exercise Sheet 13 here.
Content:
- Time Complexity
- P,NP,NP-completeness
- Space Complexity
- Savitch's theorem, games
- NL, Immerman and Szlepcseny's theorem
- Diagonalization
- Hierachy theorems
- Ladner's theorem
- Parameterized Complexity
- Graphs of bounded tree width
- Courcelle's theorem
- Hardness theory
- Polynomial Hierarchy
- Definition and complete problems
- Alternation
- Collapse
- Circuits
- P/poly
- Karp and Lipton's theorem
- Lower bounds
- NC and parallel computing
- Randomness
- BPP
- Adleman's theorem
- Sipser and Gac's theorem
- Counting
- #P
- Approximate counting
- Toda's theorem
- Communication Complexity
- Fooling sets
- Logic in Complexity Theory
- Alternative definition of complexity classes
- Theories
Literature:
- M. Sipser: Introduction to the Theory of Computation. International Thomson Publishing, 1996
- I. Wegener: Complexity Theory. Springer, 2005
- D.C. Kozen: Automata and Computability. Springer, 1997
- O. Goldreich: Computational Complexity. Cambridge, 2008