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+ − <H2>2011/12 MSc Individual Projects</H2>+ −
<H4>Supervisor: Christian Urban</H4> + −
<H4>Email: christian dot urban at kcl dot ac dot uk, Office: Strand Building S6.30</H4>+ −
<H4>If you are interested in a project, please send me an email and we can discuss details. Please include+ −
a short description about your programming skills and computer science background in your first email. + −
I will also need your King's username in order to book the project for you. Thanks.</H4> + −
+ − <ul class="striped">+ −
<li> <H4>[CU1] Implementing a SAT-Solver in a Functional Programming Language</H4>+ −
+ − <p><B>Description:</b> + −
SAT-solver search for satisfying assignments of boolean formulas. Although this + −
is a computationally hard problem (<A HREF="http://en.wikipedia.org/wiki/NP-complete">NP-complete</A>), + −
modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables. + −
Application areas of SAT-solver are manifold: they range from hardware verification to + −
Sudoku solvers (see <a href="http://anytime.cs.umass.edu/aimath06/proceedings/P34.pdf">here</a>). + −
Every 2 years there is a competition of the best SAT-solvers in the world.</p> + −
+ − <p>+ −
Most SAT-solvers are written in C. The aim of this project is to design and implement + −
a SAT-solver in a functional programming language (preferably + −
<A HREF="http://en.wikipedia.org/wiki/Standard_ML">ML</A>, but + −
<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>, + −
<A HREF="http://www.scala-lang.org/">Scala</A>,+ −
<A HREF="http://caml.inria.fr/">OCaml</A>, ... are also OK). Starting point is + −
the open source SAT-solver MiniSat (available <A HREF="http://minisat.se/Main.html">here</A>). + −
The long-term hope is that your implementation becomes part of the interactive theorem prover + −
<A HREF="http://www.cl.cam.ac.uk/research/hvg/isabelle/">Isabelle</A>. For this+ −
the SAT-solver needs to be implemented in ML.</p> + −
+ − <p>+ −
<B>Tasks:</B> Understand MiniSat, design and code a SAT-solver in ML, + −
empirical evaluation and tuning of your code.</p>+ −
+ − <p>+ −
<B>Literature:</B> A good starting point for reading about SAT-solving is the handbook+ −
article <A HREF="http://www.cs.cornell.edu/gomes/papers/SATSolvers-KR-Handbook.pdf">here</A>.+ −
MiniSat is explained <A HREF="http://minisat.se/downloads/MiniSat.pdf">here</A> and+ −
<A HREF="http://minisat.se/Papers.html">here</A>. The standard reference for ML is+ −
<A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy + −
of this book for the duration of the project). The best free implementation of ML is + −
<A HREF="http://www.polyml.org/">PolyML</A>.+ −
</p>+ −
+ − <li> <H4>[CU2] A Compiler for System F</H4>+ −
+ − <p><b>Description:</b> + −
<A HREF="http://en.wikipedia.org/wiki/System_F">System F</A> is a mini programming language, + −
which is often used to study the theory behind programming languages, but is also used as + −
a core-language of functional programming languages (for example + −
<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>). The language is small+ −
enough to implement in a reasonable amount of time a compiler to an+ −
idealised assembly language (preferably + −
<A HREF="http://en.wikipedia.org/wiki/Typed_assembly_language">TAL</A>) or an abstract machine.+ −
This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette+ −
(available in English <A HREF="https://papyrus.bib.umontreal.ca/jspui/bitstream/1866/3454/6/Guillemette_Louis-Julien_2009_these.pdf">here</A>). He used <A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>+ −
as his implementation language. Other choices are possible.+ −
</p>+ −
+ − <p>+ −
<b>Tasks:</b>+ −
Read the relevant literature and implement the various components of a compiler+ −
(parser, intermediate languages, simulator for the idealised assembly language).+ −
This project is for a good student with an interest in programming languages,+ −
who can also translate abstract ideas into code. If it is too difficult, the project can+ −
be easily scaled down to the + −
<A HREF="http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus">simply-typed + −
lambda calculus</A> (which is simpler than+ −
System F) or to cover only some components of the compiler.+ −
</p> + −
+ − <p>+ −
<B>Literature:</B>+ −
The <A HREF="https://papyrus.bib.umontreal.ca/jspui/bitstream/1866/3454/6/Guillemette_Louis-Julien_2009_these.pdf">PhD-thesis</A> by Louis-Julien Guillemette is required reading. A shorter+ −
paper about this subject is available <A HREF="http://www.iro.umontreal.ca/~monnier/icfp08.pdf">here</A>.+ −
A good starting point for TAL is <A HREF="http://www.cs.cornell.edu/talc/papers/tal-tr.pdf">here</A>.+ −
There is a lot of literature about compilers + −
(for example <A HREF="http://www.cs.princeton.edu/~appel/papers/cwc.html">this book</A> -+ −
I can lend you my copy for the duration of the project). A very good overview article+ −
about implementing compilers by + −
<A HREF="http://tratt.net/laurie/">Laurie Tratt</A> is + −
<A HREF="http://tratt.net/laurie/tech_articles/articles/how_difficult_is_it_to_write_a_compiler">here</A>.+ −
</p>+ −
+ − <li> <H4>[CU3] Sorting Suffixes</H4>+ −
+ −
<p><b>Description:</b> Given a string, take all its suffixes, and sort them.+ −
This is often called <A HREF="http://en.wikipedia.org/wiki/Suffix_array">suffix + −
array sorting</A>. It sound simple, but there are some difficulties. + −
The naive algorithm would generate all suffix strings and sort them+ −
using a standard sorting algorithm, for example + −
<A HREF="http://en.wikipedia.org/wiki/Quicksort">quicksort</A>. + −
The problem is that+ −
this algorithm is not optimal for suffix sorting: it does not take into account that you sort+ −
suffixes and it also takes a quadratic amount of space. This is a + −
huge problem if you have to sort strings of several Megabytes or even Gigabytes,+ −
as happens often in biotech and DNA data mining. Suffix sorting is also a crucial operation for the + −
<A HREF="http://en.wikipedia.org/wiki/Burrows-Wheeler_transform">Burrows-Wheeler transform</A>+ −
on which the data compression algorithm of the popular + −
<A HREF="http://en.wikipedia.org/wiki/Bzip2">bzip2</A>+ −
program is based.+ −
</p>+ −
+ − <p>+ −
There are more efficient algorithms for suffix sorting, for example + −
<A HREF="http://books.google.co.uk/books?id=Pn1sHToYf9oC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false">here</A> and + −
<A HREF="http://ls11-www.cs.uni-dortmund.de/people/rahmann/teaching/ss2008/AlgorithmenAufSequenzen/09-walk-bwt.pdf">here</A>. + −
However the most space efficient algorithm for suffix sorting + −
(<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">here</A>) + −
is horrendously complicated. Your task would be to understand it, and then implement it.+ −
</p>+ −
+ −
<p>+ −
<B>Tasks:</B>+ −
Start by reading the literature about suffix sorting. Then work through the+ −
12-page <A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">paper</A> + −
explaining the horrendously complicated algorithm and implement it.+ −
Time permitting the work can include an implementation of the Burrows-Wheeler + −
data compression. This project is for a good student, who likes to study in-depth + −
algorithms. The project can be carried out in almost all programming languages,+ −
including C, Java, Scala, ML, Haskell and so on.+ −
</p>+ −
+ − <p>+ −
<B>Literature:</B> A good starting point for reading about suffix sorting is the + −
<A HREF="http://books.google.co.uk/books?id=Pn1sHToYf9oC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false">book</A> by Crochemore. + −
Another good introduction is + −
<A HREF="http://people.unipmn.it/manzini/papers/esa02.pdf">here</A>, + −
which gives also good pointers for why efficient suffix sorting+ −
is practically relevant.+ −
Two simple algorithms are described+ −
<A HREF="http://ls11-www.cs.uni-dortmund.de/people/rahmann/teaching/ss2008/AlgorithmenAufSequenzen/09-walk-bwt.pdf">here</A>. The main literature is the 12-page+ −
<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">article</A> about in-place+ −
suffix sorting. The Burrows-Wheeler data compression is described + −
<A HREF="http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pdf">here</A>.+ −
</p>+ −
+ − <li> <H4>[CU4] Simplification with Equivalence Relations in the Isabelle Theorem Prover</H4>+ −
<p>+ −
<B>Description:</B>+ −
In this project you have to extend the simplifier of the + −
<A HREF="http://isabelle.in.tum.de/">Isabelle theorem prover</A>. + −
The simplifier is an important reasoning tool of this theorem prover: it + −
replaces a term by another term that can be proved to be equal to it. However, + −
currently the simplifier only rewrites terms according to equalities. + −
Assuming ≈ is an equivalence relation, the simplifier should also be able + −
to rewrite terms according to ≈. Since equivalence relations occur + −
frequently in automated reasoning, this extension would make the simplifier + −
more powerful and useful. The hope is that your code can go into the+ −
code base of Isabelle.+ −
</p>+ −
+ − <p>+ −
<B>Tasks:</B> + −
Read the <A HREF="http://www.springerlink.com/content/x7041m1807738832/">paper</A>+ −
about rewriting with equivalence relations. Get familiar with parts of the + −
implementation of Isabelle (I will be of much help as I can). Implement+ −
the extension. This project is suitable for a student with a bit of math background.+ −
It requires knowledge of the functional programming language ML, which+ −
however can be learned quickly provided you have already written code+ −
in another functional programming language.+ −
</p>+ −
+ − <p>+ −
<B>Literature:</B> A good starting point for reading about rewriting modulo equivalences + −
is the paper <A HREF="http://www.springerlink.com/content/x7041m1807738832/">here</A>, + −
which uses the ACL2 theorem prover. The implementation of the Isabelle theorem+ −
prover is described in much detail in this + −
<A HREF="http://www.inf.kcl.ac.uk/staff/urbanc/Cookbook/">programming tutorial</A>.+ −
The standard reference for ML is+ −
<A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy + −
of this book for the duration of the project).+ −
</p>+ −
+ − + − <li><h4>[CU5] Lexing and Parsing with Derivatives</h4>+ −
+ − <p>+ −
<B>Description:</B>+ −
Lexing and parsing are usually done using automated tools, like + −
<A HREF="http://en.wikipedia.org/wiki/Lex_programming_tool">lex</A> and + −
<A HREF="http://en.wikipedia.org/wiki/Yacc">yacc</A>. The problem + −
with them is that they "work when they work", but if they do not, then they are+ −
<A HREF="http://en.wikipedia.org/wiki/Black_box">black boxes</A>+ −
which are difficult to debug and change. They are really quite + −
clumsy to the point that Might and Darais wrote a paper titled + −
"<A HREF="http://arxiv.org/pdf/1010.5023v1">Yacc is dead</A>".</p>+ −
+ −
<p>+ −
There is a simple algorithm for regular expression matching (that is lexing).+ −
This algorithm was introduced by + −
<A HREF="http://en.wikipedia.org/wiki/Janusz_Brzozowski_(computer_scientist)">Brzozowski</A> + −
in 1964. It is based on the notion of derivatives of regular expressions and + −
has proved <A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">useful</A> + −
for practical lexing. Last year the notion of derivatives was extended by + −
<A HREF="http://matt.might.net/papers/might2011derivatives.pdf">Might et al</A>+ −
to <A HREF="http://en.wikipedia.org/wiki/Context-free_grammar">context free grammars</A> + −
and parsing.+ −
</p> + −
+ −
<p>+ −
<B>Tasks:</B> Get familiar with the two algorithms and implement them. Regular+ −
expression matching is relatively simple; parsing with derivatives is the + −
harder part. Therefore you should empirically evaluate this part and+ −
tune your implementation. The project can be carried out in almost all programming + −
languages, including C, Java, Scala, ML, Haskell and so on.+ −
</p>+ −
+ − <p>+ −
<B>Literature:</B> This + −
<A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">paper</A> + −
gives a modern introduction to derivative based lexing. Derivative-based+ −
parsing is explained <A HREF="http://arxiv.org/pdf/1010.5023v1">here</A>+ −
and <A HREF="http://matt.might.net/papers/might2011derivatives.pdf">here</A>.+ −
A proposal for derivative PEG-parsing is + −
<A HREF="http://fmota.eu/2011/01/07/PEG-derivatives.html">here</a>. The mailing+ −
list about PEGs is <A HREF="https://lists.csail.mit.edu/pipermail/peg/">here</A>.+ −
</p> + −
+ − <li> <H4>[CU6] Equivalence Checking of Regular Expressions using the Method by Antimirov and Mosses</H4>+ −
+ − <p>+ −
<B>Description:</B> + −
Solving the problem of deciding equivalence of regular expressions can be used+ −
to decide a number of problems in automated reasoning. Therefore one likes to+ −
have a method for equivalence checking that is as fast as possible. There have+ −
been a number of algorithms proposed in the past, but one based on a method+ −
by Antimirov and Mosses seems relatively simple and easy to implement.+ −
</p> + −
+ −
<p>+ −
<B>Tasks:</B>+ −
The task is to implement the algorithm by Antimirov and Mosses and compare it to+ −
other methods. Hopefully the algorithm can be tuned to be faster than other+ −
methods. The project can be carried out in almost all programming languages, but+ −
as usual functional programming languages such Scala, ML, Haskell have an edge+ −
for this kind of problems.+ −
</p>+ −
+ − <p>+ −
<B>Literature:</B>+ −
Central to this project are the papers <A HREF="http://www.dcc.fc.up.pt/~nam/publica/ijcs08.pdf">here</A>+ −
and <A HREF="http://www.dcc.fc.up.pt/~nam/publica/51480046.pdf">here</A>.+ −
Other methods have been described, for example, + −
<A HREF="http://www4.informatik.tu-muenchen.de/~krauss/papers/rexp.pdf">here</A>.+ −
A relatively complicated method, based on automata, is described + −
<A HREF="http://sardes.inrialpes.fr/~braibant/atbr/">here</A>.+ −
</p> + −
+ − <li> <H4>[CU7] Game-Playing Engine for Five-In-A-Row on a Large Board</H4>+ −
+ − <p>+ −
<B>Literature:</b>+ −
There is a web-page with various pointers to computer players+ −
<A HREF="http://webdocs.cs.ualberta.ca/~games/">here</A>. There are+ −
also some good books about computer players, for example:+ −
<table cellspacing="10">+ −
<tr><td><i>Artificial Intelligence: A Modern Approach</i> by S. Russel and P. Norvig, Prentice Hall, 2003 + −
(a standard textbook about search strategies).+ −
</td></tr>+ −
<tr><td><i>Principles of Artificial Intelligence</i> by N. J. Nilsson, Springer Verlag, 1980 + −
(a standard textbook about search strategies).+ −
</td></tr>+ −
+ − <tr><td><i>Computer Game-Playing: Theory and Practice</i> by M. Bramer, Ellis Horwood Ltd, 1983+ −
(considers techniques used for programming a variety of games: Chess, Go, Scrabble, Billiards, + −
Othello, etc; includes theoretical issues about game searching).+ −
</td></tr>+ −
<tr><td><i>Chips Challenging Champions: Games, Computers and Artificial Intelligence</i> by+ −
J. Schaeffer and H.J. van den Herik, North Holland, 2002.+ −
</td></tr>+ −
<tr><td>+ −
<i>Artificial Intelligence for Games</i> by I. Millington and J. Funge, Morgan Kaufmann, 2009.+ −
</td></tr>+ −
<tr><td>+ −
<i>Computer Gamesmanship: The Complete Guide to Creating and Structuring Intelligent Games Programs</i> + −
by D.N.L. Levy, Simon and Schuster, 1983.+ −
</td></tr>+ −
</table>+ −
</p>+ −
+ − <li><h4>[CU8] Webserver for a Revision Control System</h4>+ −
+ − <p>+ −
Modern revision control systems are+ −
<A HREF="http://mercurial.selenic.com/">mercurial</A> and+ −
<A HREF="http://git-scm.com/">git</A>.+ −
</p>+ −
+ − <p>+ −
<b>Task:</b> Build a webserver for a revision control system + −
that allows user management. + −
</p>+ −
+ − </ul>+ −
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