| author | Christian Urban <urbanc@in.tum.de> |
| Mon, 12 Dec 2011 11:01:11 +0000 | |
| changeset 51 | f14fa1742f36 |
| parent 50 | 37e9d1eb8004 |
| child 54 | 7386f513c412 |
| permissions | -rw-r--r-- |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
1 |
<?xml version="1.0" encoding="utf-8"?> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
2 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
3 |
<HEAD> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
4 |
<TITLE>Christian Urban</TITLE> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
5 |
<BASE HREF="http://www.inf.kcl.ac.uk/staff/urbanc/"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
6 |
<script type="text/javascript" src="striper.js"></script> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
7 |
<link rel="stylesheet" href="nominal.css"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
8 |
</HEAD> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
9 |
<BODY TEXT="#000000" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
10 |
BGCOLOR="#4169E1" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
11 |
LINK="#0000EF" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
12 |
VLINK="#51188E" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
13 |
ALINK="#FF0000" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
14 |
ONLOAD="striper('ul','striped','li','first,second')">
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
15 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
16 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
17 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
18 |
<TABLE WIDTH="100%" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
19 |
BGCOLOR="#4169E1" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
20 |
BORDER="0" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
21 |
FRAME="border" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
22 |
CELLPADDING="10" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
23 |
CELLSPACING="2" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
24 |
RULES="all"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
25 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
26 |
<TR> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
27 |
<TD BGCOLOR="#FFFFFF" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
28 |
WIDTH="75%" |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
29 |
VALIGN="TOP"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
30 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
31 |
<H2>2011/12 MSc Individual Projects</H2> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
32 |
<H4>Supervisor: Christian Urban</H4> |
| 47 | 33 |
<H4>Email: christian dot urban at kcl dot ac dot uk, Office: Strand Building S6.30</H4> |
34 |
<H4>If you are interested in a project, please send me an email and we can discuss details. Please include |
|
| 50 | 35 |
a short description about your programming skills and computer science background in your first email. |
36 |
I will also need your King's username in order to book the project for you. Thanks.</H4> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
37 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
38 |
<ul class="striped"> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
39 |
<li> <H4>[CU1] Implementing a SAT-Solver in a Functional Programming Language</H4> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
40 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
41 |
<p><B>Description:</b> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
42 |
SAT-solver search for satisfying assignments of boolean formulas. Although this |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
43 |
is a computationally hard problem (<A HREF="http://en.wikipedia.org/wiki/NP-complete">NP-complete</A>), |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
44 |
modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables. |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
45 |
Application areas of SAT-solver are manifold: they range from hardware verification to |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
46 |
Sudoku solvers. Every 2 years there is a competition of the best SAT-solvers in the world.</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
47 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
48 |
<p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
49 |
Most SAT-solvers are written in C. The aim of this project is to design and implement |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
50 |
a SAT-solver in a functional programming language (preferably |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
51 |
<A HREF="http://en.wikipedia.org/wiki/Standard_ML">ML</A>, but |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
52 |
<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>, |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
53 |
<A HREF="http://www.scala-lang.org/">Scala</A>, |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
54 |
<A HREF="http://caml.inria.fr/">OCaml</A>, ... are also OK). Starting point is |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
55 |
the open source SAT-solver MiniSat (available <A HREF="http://minisat.se/Main.html">here</A>). |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
56 |
The long-term hope is that your implementation becomes part of the interactive theorem prover |
| 44 | 57 |
<A HREF="http://www.cl.cam.ac.uk/research/hvg/isabelle/">Isabelle</A>. For this |
58 |
the SAT-solver needs to be implemented in ML.</p> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
59 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
60 |
<p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
61 |
<B>Tasks:</B> Understand MiniSat, design and code a SAT-solver in ML, |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
62 |
empirical evaluation and tuning of your code.</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
63 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
64 |
<p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
65 |
<B>Literature:</B> A good starting point for reading about SAT-solving is the handbook |
| 44 | 66 |
article <A HREF="http://www.cs.cornell.edu/gomes/papers/SATSolvers-KR-Handbook.pdf">here</A>. |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
67 |
MiniSat is explained <A HREF="http://minisat.se/downloads/MiniSat.pdf">here</A> and |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
68 |
<A HREF="http://minisat.se/Papers.html">here</A>. The standard reference for ML is |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
69 |
<A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
70 |
of this book for the duration of the project). The best free implementation of ML is |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
71 |
<A HREF="http://www.polyml.org/">PolyML</A>. |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
72 |
</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
73 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
74 |
<li> <H4>[CU2] A Compiler for System F</H4> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
75 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
76 |
<p><b>Description:</b> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
77 |
<A HREF="http://en.wikipedia.org/wiki/System_F">System F</A> is a mini programming language, |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
78 |
which is often used to study the theory behind programming languages, but is also used as |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
79 |
a core-language of functional programming languages (for example |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
80 |
<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>). The language is small |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
81 |
enough to implement in a reasonable amount of time a compiler to an |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
82 |
idealised assembly language (preferably |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
83 |
<A HREF="http://en.wikipedia.org/wiki/Typed_assembly_language">TAL</A>) or an abstract machine. |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
84 |
This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
85 |
(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> |
| 44 | 86 |
as his implementation language. Other choices are possible. |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
87 |
</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
88 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
89 |
<p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
90 |
<b>Tasks:</b> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
91 |
Read the relevant literature and implement the various components of a compiler |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
92 |
(parser, intermediate languages, simulator for the idealised assembly language). |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
93 |
This project is for a good student with an interest in programming languages, |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
94 |
who can also translate abstract ideas into code. If it is too difficult, the project can |
| 44 | 95 |
be easily scaled down to the |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
96 |
<A HREF="http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus">simply-typed |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
97 |
lambda calculus</A> (which is simpler than |
| 44 | 98 |
System F) or to cover only some components of the compiler. |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
99 |
</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
100 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
101 |
<p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
102 |
<B>Literature:</B> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
103 |
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 |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
104 |
paper about this subject is available <A HREF="http://www.iro.umontreal.ca/~monnier/icfp08.pdf">here</A>. |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
105 |
A good starting point for TAL is <A HREF="http://www.cs.cornell.edu/talc/papers/tal-tr.pdf">here</A>. |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
106 |
There is a lot of literature about compilers |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
107 |
(for example <A HREF="http://www.cs.princeton.edu/~appel/papers/cwc.html">this book</A> - |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
108 |
I can lend you my copy for the duration of the project). |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
109 |
</p> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
110 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
111 |
<li> <H4>[CU3] Sorting Suffixes</H4> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
112 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
113 |
<p><b>Description:</b> Given a string, take all its suffixes, and sort them. |
| 44 | 114 |
This is often called <A HREF="http://en.wikipedia.org/wiki/Suffix_array">suffix |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
115 |
array sorting</A>. It sound simple, but there are some difficulties. |
| 44 | 116 |
The naive algorithm would generate all suffix strings and sort them |
117 |
using a standard sorting algorithm, for example |
|
118 |
<A HREF="http://en.wikipedia.org/wiki/Quicksort">quicksort</A>. |
|
119 |
The problem is that |
|
120 |
this algorithm is not optimal for suffix sorting: it does not take into account that you sort |
|
121 |
suffixes and it also takes a quadratic amount of space. This is a |
|
122 |
huge problem if you have to sort strings of several Megabytes or even Gigabytes, |
|
123 |
as happens often in biotech and DNA data mining. Suffix sorting is also a crucial operation for the |
|
| 51 | 124 |
<A HREF="http://en.wikipedia.org/wiki/Burrows-Wheeler_transform">Burrows-Wheeler transform</A> |
| 44 | 125 |
on which the data compression algorithm of the popular |
126 |
<A HREF="http://en.wikipedia.org/wiki/Bzip2">bzip2</A> |
|
127 |
program is based. |
|
128 |
</p> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
129 |
|
| 44 | 130 |
<p> |
131 |
There are more efficient algorithms for suffix sorting, for example |
|
132 |
<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 |
|
133 |
<A HREF="http://ls11-www.cs.uni-dortmund.de/people/rahmann/teaching/ss2008/AlgorithmenAufSequenzen/09-walk-bwt.pdf">here</A>. |
|
134 |
However the most space efficient algorithm for suffix sorting |
|
135 |
(<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">here</A>) |
|
136 |
is horrendously complicated. Your task would be to understand it, and then implement it. |
|
137 |
</p> |
|
138 |
||
139 |
<p> |
|
140 |
<B>Tasks:</B> |
|
141 |
Start by reading the literature about suffix sorting. Then work through the |
|
142 |
12-page <A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">paper</A> |
|
143 |
explaining the horrendously complicated algorithm and implement it. |
|
144 |
Time permitting the work can include an implementation of the Burrows-Wheeler |
|
145 |
data compression. This project is for a good student, who likes to study in-depth |
|
146 |
algorithms. The project can be carried out in almost all programming languages, |
|
147 |
including C, Java, Scala, ML, Haskell and so on. |
|
148 |
</p> |
|
149 |
||
150 |
<p> |
|
151 |
<B>Literature:</B> A good starting point for reading about suffix sorting is the |
|
152 |
<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. Two simple algorithms are also described |
|
153 |
<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 |
|
154 |
<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">article</A> about in-place |
|
155 |
suffix sorting. The Burrows-Wheeler data compression is described |
|
156 |
<A HREF="http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pdf">here</A>. |
|
157 |
</p> |
|
158 |
||
159 |
<li> <H4>[CU4] Simplification with Equivalence Relations in the Isabelle Theorem Prover</H4> |
|
160 |
<p> |
|
161 |
<B>Description:</B> |
|
162 |
In this project you have to extend the simplifier of the |
|
163 |
<A HREF="http://isabelle.in.tum.de/">Isabelle theorem prover</A>. |
|
164 |
The simplifier is an important reasoning tool of this theorem prover: it |
|
165 |
replaces a term by another term that can be proved to be equal to it. However, |
|
166 |
currently the simplifier only rewrites terms according to equalities. |
|
167 |
Assuming ≈ is an equivalence relation, the simplifier should also be able |
|
168 |
to rewrite terms according to ≈. Since equivalence relations occur |
|
169 |
frequently in automated reasoning, this extension would make the simplifier |
|
170 |
more powerful and useful. The hope is that your code can go into the |
|
171 |
code base of Isabelle. |
|
172 |
</p> |
|
173 |
||
174 |
<p> |
|
175 |
<B>Tasks:</B> |
|
176 |
Read the <A HREF="http://www.springerlink.com/content/x7041m1807738832/">paper</A> |
|
177 |
about rewriting with equivalence relations. Get familiar with parts of the |
|
178 |
implementation of Isabelle (I will be of much help as I can). Implement |
|
179 |
the extension. This project is suitable for a student with a bit of math background. |
|
180 |
It requires knowledge of the functional programming language ML, which |
|
181 |
however can be learned quickly provided you have already written code |
|
182 |
in another functional programming language. |
|
183 |
</p> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
184 |
|
| 44 | 185 |
<p> |
186 |
<B>Literature:</B> A good starting point for reading about rewriting modulo equivalences |
|
187 |
is the paper <A HREF="http://www.springerlink.com/content/x7041m1807738832/">here</A>, |
|
188 |
which uses the ACL2 theorem prover. The implementation of the Isabelle theorem |
|
189 |
prover is described in much detail in this |
|
190 |
<A HREF="http://www.inf.kcl.ac.uk/staff/urbanc/Cookbook/">programming tutorial</A>. |
|
191 |
The standard reference for ML is |
|
192 |
<A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
|
193 |
of this book for the duration of the project). |
|
194 |
</p> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
195 |
|
| 44 | 196 |
|
197 |
<li><h4>[CU5] Lexing and Parsing with Derivatives</h4> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
198 |
|
| 44 | 199 |
<p> |
200 |
<B>Description:</B> |
|
201 |
Lexing and parsing are usually done using automated tools, like |
|
202 |
<A HREF="http://en.wikipedia.org/wiki/Lex_programming_tool">lex</A> and |
|
203 |
<A HREF="http://en.wikipedia.org/wiki/Yacc">yacc</A>. The problem |
|
| 47 | 204 |
with them is that they "work when they work", but if they do not, then they are |
| 44 | 205 |
<A HREF="http://en.wikipedia.org/wiki/Black_box">black boxes</A> |
206 |
which are difficult to debug and change. They are really quite |
|
| 47 | 207 |
clumsy to the point that Might and Darais wrote a paper titled |
| 44 | 208 |
"<A HREF="http://arxiv.org/pdf/1010.5023v1">Yacc is dead</A>".</p> |
209 |
||
210 |
<p> |
|
| 47 | 211 |
There is a simple algorithm for regular expression matching (that is lexing). |
| 44 | 212 |
This algorithm was introduced by |
213 |
<A HREF="http://en.wikipedia.org/wiki/Janusz_Brzozowski_(computer_scientist)">Brzozowski</A> |
|
214 |
in 1964. It is based on the notion of derivatives of regular expressions and |
|
215 |
has proved <A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">useful</A> |
|
216 |
for practical lexing. Last year the notion of derivatives was extended by |
|
217 |
<A HREF="http://matt.might.net/papers/might2011derivatives.pdf">Might et al</A> |
|
218 |
to <A HREF="http://en.wikipedia.org/wiki/Context-free_grammar">context free grammars</A> |
|
219 |
and parsing. |
|
220 |
</p> |
|
221 |
||
222 |
<p> |
|
223 |
<B>Tasks:</B> Get familiar with the two algorithms and implement them. Regular |
|
224 |
expression matching is relatively simple; parsing with derivatives is the |
|
225 |
harder part. Therefore you should empirically evaluate this part and |
|
226 |
tune your implementation. The project can be carried out in almost all programming |
|
227 |
languages, including C, Java, Scala, ML, Haskell and so on. |
|
228 |
</p> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
229 |
|
| 44 | 230 |
<p> |
231 |
<B>Literature:</B> This |
|
232 |
<A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">paper</A> |
|
233 |
gives a modern introduction to derivative based lexing. Derivative-based |
|
234 |
parsing is explained <A HREF="http://arxiv.org/pdf/1010.5023v1">here</A> |
|
235 |
and <A HREF="http://matt.might.net/papers/might2011derivatives.pdf">here</A>. |
|
236 |
</p> |
|
237 |
||
238 |
<li> <H4>[CU6] Equivalence Checking of Regular Expressions using the Method by Antimirov and Mosses</H4> |
|
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
239 |
|
| 44 | 240 |
<p> |
241 |
<B>Description:</B> |
|
242 |
Solving the problem of deciding equivalence of regular expressions can be used |
|
243 |
to decide a number of problems in automated reasoning. Therefore one likes to |
|
| 47 | 244 |
have a method for equivalence checking that is as fast as possible. There have |
245 |
been a number of algorithms proposed in the past, but one based on a method |
|
246 |
by Antimirov and Mosses seems relatively simple and easy to implement. |
|
| 44 | 247 |
</p> |
248 |
||
249 |
<p> |
|
250 |
<B>Tasks:</B> |
|
251 |
The task is to implement the algorithm by Antimirov and Mosses and compare it to |
|
252 |
other methods. Hopefully the algorithm can be tuned to be faster than other |
|
| 47 | 253 |
methods. The project can be carried out in almost all programming languages, but |
254 |
as usual functional programming languages such Scala, ML, Haskell have an edge |
|
255 |
for this kind of problems. |
|
| 44 | 256 |
</p> |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
257 |
|
| 44 | 258 |
<p> |
259 |
<B>Literature:</B> |
|
260 |
Central to this project is the paper <A HREF="http://www.dcc.fc.up.pt/~nam/publica/ijcs08.pdf">here</A>. |
|
261 |
Other methods have been described, for example, |
|
262 |
<A HREF="http://www4.informatik.tu-muenchen.de/~krauss/papers/rexp.pdf">here</A>. |
|
| 47 | 263 |
A relatively complicated method, based on automata, is described |
264 |
<A HREF="http://sardes.inrialpes.fr/~braibant/atbr/">here</A>. |
|
| 44 | 265 |
</p> |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
266 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
267 |
</ul> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
268 |
</TD> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
269 |
</TR> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
270 |
</TABLE> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
271 |
|
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
272 |
<P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 --> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
273 |
<!-- hhmts start --> |
| 51 | 274 |
Last modified: Mon Dec 12 11:00:43 GMT 2011 |
|
43
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
275 |
<!-- hhmts end --> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
276 |
<a href="http://validator.w3.org/check/referer">[Validate this page.]</a> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
277 |
</BODY> |
|
a6c077ba850a
added initial version of projects
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
278 |
</HTML> |