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Computability and Complexity, Spring 2015

Computability and Complexity (320352)

Jacobs University Bremen, Spring 2015, Herbert Jaeger

Class sessions: Thursdays and Fridays 14:15 – 15:30

Course description. This lecture presents one half of the core material of theoretical computer science (the other half is covered in the lecture "Formal Languages and Logic''). The question: "What problems can a computer possibly solve?'', is fully answered (by characterizing those solvable problems, equivalently, through Turing machines, random access machines, recursive functions and lambda calculus). A full answer to the related question, "how much computational resources are needed for solving a given problem'' is not known today. However, the basic outlines of today's theory of computational complexity will be presented up to the most famous open problem in computer science, namely the famous "P = NP'' question: if a computer can guess the answer to a problem (and only needs to check its correctness), does that really help to speed up computation?

Course culture. Like in FLL in Fall, the basic idea is that participants pre-read the daily material, which is then rehearsed in the first part of a classroom session, after which I will reserve time to classroom interaction, by asking simple, advanced or outlandish questions, going through miniexercises, present add-on material, etc. 10% of the final grade will be based on classroom participation. A good way to reliably score high in this respect is to think of classroom questions while you are doing the pre-reading. Questions can be just mere requests for clarification of the technical contents of the reading, but also probing deep, be about the context of the taught material, challenging me, bewildering classmates. The more we get seriously challenged, the better the question. Classroom presence is mandatory.

Homeworks. Students can work in singles or as teams of two but not larger. HWs count 10 % of the course score. Homework sheets are not graded in the usual sense. Instead, a HW sheet gets a full score if all problems have been visibly and convincingly worked on. Correctness of solutions is not required for full scores. It is permissible (though unwise) to copy solutions from friends or other sources.  In this case, the fact that the solutions are copied, as well as the source, must be stated on the HW sheet. TA's will annotate HW sheets that are original work (not copied) to provide useful feedback. If a student copies the solutions and does not indicate that fact and the source, it will be treated as a cheating case (nulling the sheet, notification of the Office of Academic Affairs).

Lecture Notes are here.

For exam preparation, previous finals with solutions from years 2004, 2006, 2008 are here. An exam in the multiple-choice format from 2010 is here.

References

  • Papadimitriou, C: Computational Complexity, (Addison-Wesley) IRC: QA267.7 .P36 1994
  • Hopcroft, John E. , Motwani, Rajeev, and Ullman, Jeffrey: Introduction to Automata Theory, 2nd (Addison-Wesley) IRC: QA267 .H56 2001
  • Garey, Michael and Johnson, David: Computers and Intractability: A guide to the Theory of NP-completeness (Macmillan) IRC: QA76.6 .G35

Grading and exams: The final course grade will be composed from homeworks (10%), presence sheets (10%), active participation in class (5%), and quizzes/exams. There will be four miniquizzes (written in class, 20 minutes), the best three of which will each account to 15% of the final grade (worst will be dropped from calculating the grade), and one final exam, counting 30%. All quizzes are open book.

Miniquiz makeup rules: if a miniquiz is missed without excuse, it will be graded with 0 points. A makeup will be offered for medically excused miniquizzes according to the Jacobs rules (especially, the medical excuse must be announced to me before the miniquiz). Non-medical excuses can be accepted on a case-by-case basis.