600.771: Seminar in Theory
Fall Term 2004
Christian Scheideler
Meetings
The first meeting will be on Wednesday, Sep 15, at 4 p.m. in NEB 317.
Topics
This seminar course reviews current research in theoretical computer
science. Students will read, present and discuss papers in weekly
meetings. Pre-req: permission of instructor. [Analysis]
Selected Papers
- Computers program themselves
Whether the
Olivanova
Model Execution Machine can fulfill its expectations
is not yet clear. From a theoretical point of view, however,
Marcus Hutter has
presented an algorithm in 2000 that can provably solve every problem when
given a functional specification of it. Moreover, his HSEARCH algorithm
requires asymptotically at most a constant factor more time than any other
algorithm for the given problem. Under certain, weak assumptions one can
even reach a factor of 5!
- Theory of adventure games
Among the adventure games are well-known games such as Monkey Island,
Space Quest, King's Quest, and Leisure Suit Larry as well as classics
such as The Dallas Quest or /usr/games/adventure under Unix.
Brauer, Holzer, Koenig, and Schwoon have been able to come up with a nice classification
of these games. It illustrates the perhaps otherwise quite dry area of
formal languages and Chomsky hierarchy in an amusing way and implies
results about the hardness of solving adventures games.
- C++ parsers are universal
Like all practical programming languages, C++ is context-free, i.e. it can be
parsed in O(n^3) steps (when ignoring the type-checking). To identify a
correct C++ program under consideration of type-checking, however, is
Turing-complete. Surprisingly,
Boehme and Manthey have shown that already
during the compilation, every partially recursive function can be computed.
- Buechi automata are closed under complement
That a class of languages that can be accepted by a non-deterministic finite
automaton (NFA) is closed under complement can be shown by transforming the
NFA into an equivalent DFA. For languages of infinite words
(so-called w-regular languages), however, this proof method cannot be used
any more. Buechi showed in 1960 that the class of w-regular languages is
nevertheless closed under complement. Here, Ramsey's Theorem for
infinite graphs plays a crucial role.
- On the stretch factor of planar geometric path systems
Suppose one wants to go from A to B. Their distance (when traveling through
the air) may be x, but because of the way the streets are set up,
one usually has to make a detour of length dx. Certainly, d should
be as small as possible. If A and B are arbitrary nodes in a geometric graph,
then this minimization problem leads to the well-known spanners. A
spanner aims to keep the detour for any pair of nodes as small as possible
(for example, within a constant factor of their Euclidean distance). But
spanners are not planar in general. In a celebrated work,
Icking et al
have shown upper and lower bounds for this problems concerning the
detour value (or stretch factor) d and uses a lot of interesting
geometry for this.
- Quantum time-space tradeoffs for sorting
While it is known that a quantum algorithm based on comparisons alone
cannot outperform classical sorting algorithms by more than a constant
factor in time complexity, this is wrong in a space bounded setting.
For sequential computers the time-space tradeoff for sorting is well
known to be T*S = Omega(n^2), but
Klauck
has shown that for quantum
computers this tradeoff is only T*S = Omega(n^3/2).
- Zero-knowledge proof systems
How can one prove a fact without revealing the fact itself? In his
award-winning PhD thesis,
Spielman
has shown how it is possible to reveal
every detail of the proof, yet the proved facts are kept secret.
- Microbial gene identification using interpolated Markov models
Usually, one uses pattern matching methods for identifying genes. A paper by
Salzberg,
Delcher, Kasif, and White describes how Markov chains can be used
for the identification of genes in microbial genomes.
- More topics are available on request.
Christian
Scheideler Last modified: Tue Sep 01
2004