Topics for the Spring 2009 Bachelor Theses
Wafik Lotfallah
Department of Mathematics
German University in Cairo
wafik.lotfallah@guc.edu.eg
General Research Area
The following thesis topics are taken from two different fields:
1) Deterministic/Probabilistic Search in Artificial Intelligence; and
2) Finite Model Theory, which is the branch of mathematical logic
studying the logical properties of finite mathematical structures,
and forms the main connection between logic and theoretical
computer science.
Thesis Topics
1. A guide for city driving. (1 student)
Driving in Cairo is sometimes very frustrating. First, one may miss some
shortcuts in the shortest distance path from Point A to Point B. Also, one
may end up waiting too long in a crowded street, while other routes could be
faster.
The student should write a documented program, which takes as input
a mathematical model of a city street map with maximum speed assigned to
each street at each time, together with a starting configuration (A, t 0), with t0
being the starting time, as well as an endpoint B. The program output should
be the path that the driver should take to minimize:
a) the distance travelled,
b) the time spent, or
c) the fuel consumed
(this assumes the knowledge of the fuel rate/speed function).
The student should examine different search techniques (typically studied in
courses on Artificial Intelligence), and analyze the time/space complexity of
his/her program. Also, s/he should implement the program with a reasonable
model of greater Cairo city, and examine different statistical (and other)
techniques to find the expected maximum possible speed for a given street at
a given time of the day/week/year.
2. A game capturing first order logic. (1-2 students)
The so-called Ehrenfeucht game is played on two graphs G and H by two
players, Spoiler and Duplicator. Roughly speaking, Spoiler wants to show
that G and H are different, while Duplicator wants to show that they are
actually the same. For more details, see:
http://en.wikipedia.org/wiki/Ehrenfeucht_game
In this game, Duplicator has a winning strategy in the n-round game iff G
and H agree on all sentences of first order logic of quantifier depth n.
The student(s) should write a documented program that implements this
game with a graphic interface. The program should be able to make up a
well chosen pair of graphs G and H, and play against the user. The tasks are
divided as follows:
Student #1: Is responsible for designing and writing the internal structure of
the program.
Student #2: Is responsible for the user graphic interface.