COMPLEXITY THEORY 2002/03

dr. Peter van Emde Boas

hours:
Tuesday 13.15 -- 15.--   Zaal P 017

Thursday 11.15 -- 13.--   Zaal A 303  ; starting  Feb 25  Tuesday 11.15 - 13.--  Zaal P 017.
 

Scheme of classes:

Week   Tuesday                                             Thursday

02        Jan 07    Intro: know your numbers       Jan 09   Intro:  Chapt 1 Papadimitriou
03        Jan 14    Intro: tiling puzzel                  Jan 16    Papadimitriou ch. 1 vervolg
04        Jan 21    1-tape TM model                    Jan 23      Gebruik TM model; k-tape model
05        Jan 28 (No Class: abroad)                   Jan 30 (No Class: abroad)
06        Feb 04  The 2-dim. tape case              Feb 06  No Class:  ph.d. thesis I. Vermeulen
07        Feb 11  Random Access Machines      Feb 13  Time ans Space on RAM model; Minsky theorem
08        Feb 18 (Midterm Exam weeks)          Feb 20 (Midterm Exam weeks)

STARTING FEB 25  the Thursday meeting will move to Tuesday 11.15 - 13.--  Zaal  P 017

09        Feb 25                                                Feb 25     Universal TM; Undecidability, Diagonalization methods
10        Mar 04                                                Mar 04    Abstract complexity theory, Fundamental Complexity classes
11        Mar 11                                                Mar 11    Hierarchy theorems, Savitch, Immerman-Szelepczenyi
12        Mar 18                                                 Mar 28    Elementary Reduction Theory
13        Mar 25 (Exam weeks)                         Mar 25 (Exam weeks)
14        Apr 01  (Exam weeks)                        Apr 01 (Exam weeks)
 

TheExcercise Page is now open.
 

Course Contents:

The class of mathematical problems that can be solved using a computer can be
devided into subclasses, depending on the amount of time and/or memory
required for solving these problems. There are easy and hard problems.
Given the intuitive transparency of this distinction, it is quite disappointing that
it requires serious effort to make this distinction formal. In particular,
making the difference independent of the machine model used is one of the
major achievements of the branch in computer science called Complexity Theory.

This course will focus on the basic machine models used in computation theory
and their corresponding measures for time and memory usage. The behavior of
their mutual simulations will establish the required invariance of the complexity
classes defined using these machine models.

Special attention will be given to the basic method for classifying problems
by their complexity: the reduction of one problem to another. This notion
is crucial in defining the classes  P  of tractable problems and the classes NP
and PSPACE of problems presumed to be intractable. The class  NP  is well
known on behalf of important problems included in this class like the Traveling
Salesman problem
 

Course Implementation:

The course will closely follow the book by
Papadimitriou: Computational Complexity, listed in the references below.

Don't forget to look at the excercises in the book;
they refer to lots of interesting material and some of them will be
discussed.

Sheets available:  (will be opened according to progress in class)

Topics:  Know thy  Numbers:
                Available in  Powerpoint98 format 
 

Topics:  Diagonalization and Compression:
                Available in  Powerpoint98 format  and  pdf format
 

No additional material so far has been made available for this course.
See however the material for the related courses.

Reference Material Made available in Library:  (will be extended during the course)
(don't copy copyrighted material!)

P. van Emde Boas,  Complexiteit van verzamelingenmanipulatie,
voordracht uit het MC Colloquium Capita datastructuren, MC Syllabus 37,  43 -- 63, 1978  (in Dutch).
More detailed popular expose on the role of data structures in Algorithms Design.

P. van Emde Boas, Machine Models and Simulations, form J. van Leeuwen, ed.
Handbook of Theoretical Computer Science, Vol. A, 1990, 3 -- 66.
A survey on Invariance issues in Machine models covering far more material
than chapter 2 in Papdimitriou's book.
 

Literature:  (may be extended during the course).
 

Computation Theory.

John E. Hopcroft & Jeffrey D. Ullman, Intorduction to Automata Theory,
Languages and Computation, Addison Wesley, 1979.

David Harel, Algorithmics; the Spirit of Computing, (second Edition),
Addison Wesley 1992.

A miniature version of this material appears in:
David Harel, Computers Ltd. ; what they really can't do,
Oxford Univ. Press, 2000

Thomas A. Sudkamp, Languages and Machines; An Introduction to the
Theory of Computer Science, (second Edition), Addison Wesley 1997.
the previously used textbook for the course  Automata and Complexity Theory

Harry R. Lewis & Christos H. Papadimitriou,
Elements of the Theory of Computation, Prentice Hall 1981.

Christos H. Papadimitriou, Computational Complexity,
Addison Wesley 1995.
 
 

Course Evaluation:
The course will be evaluated on the basis of homework excercises
which will be handed out during the course.

Homework excercises may be discussed in class upon expiration
of the submission deadline. Based on the problematic experiences during
the previous course electronic submission of solutions will
not be accepted.

Related courses:

dr. Peter van Emde Boas:  Theoretical Models (2nd trimester): Games and Computer Science

dr. Peter van Emde Boas:  Intelligent Databases / Game Theory (3rd trimester): Intelligent Databases