|
1 <?xml version="1.0" encoding="utf-8"?> |
|
2 <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> |
|
3 <HEAD> |
|
4 <TITLE>Christian Urban</TITLE> |
|
5 <BASE HREF="http://www.inf.kcl.ac.uk/staff/urbanc/"> |
|
6 <script type="text/javascript" src="striper.js"></script> |
|
7 <link rel="stylesheet" href="nominal.css"> |
|
8 </HEAD> |
|
9 <BODY TEXT="#000000" |
|
10 BGCOLOR="#4169E1" |
|
11 LINK="#0000EF" |
|
12 VLINK="#51188E" |
|
13 ALINK="#FF0000" |
|
14 ONLOAD="striper('ul','striped','li','first,second')"> |
|
15 |
|
16 |
|
17 |
|
18 <TABLE WIDTH="100%" |
|
19 BGCOLOR="#4169E1" |
|
20 BORDER="0" |
|
21 FRAME="border" |
|
22 CELLPADDING="10" |
|
23 CELLSPACING="2" |
|
24 RULES="all"> |
|
25 |
|
26 <TR> |
|
27 <TD BGCOLOR="#FFFFFF" |
|
28 WIDTH="75%" |
|
29 VALIGN="TOP"> |
|
30 |
|
31 <H2>2011/12 MSc Individual Projects</H2> |
|
32 <H4>Supervisor: Christian Urban</H4> |
|
33 <H4>Email: @kcl Office: Strand Building S6.30</H4> |
|
34 |
|
35 <ul class="striped"> |
|
36 <li> <H4>[CU1] Implementing a SAT-Solver in a Functional Programming Language</H4> |
|
37 |
|
38 <p><B>Description:</b> |
|
39 SAT-solver search for satisfying assignments of boolean formulas. Although this |
|
40 is a computationally hard problem (<A HREF="http://en.wikipedia.org/wiki/NP-complete">NP-complete</A>), |
|
41 modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables. |
|
42 Application areas of SAT-solver are manifold: they range from hardware verification to |
|
43 Sudoku solvers. Every 2 years there is a competition of the best SAT-solvers in the world.</p> |
|
44 |
|
45 <p> |
|
46 Most SAT-solvers are written in C. The aim of this project is to design and implement |
|
47 a SAT-solver in a functional programming language (preferably |
|
48 <A HREF="http://en.wikipedia.org/wiki/Standard_ML">ML</A>, but |
|
49 <A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>, |
|
50 <A HREF="http://www.scala-lang.org/">Scala</A>, |
|
51 <A HREF="http://caml.inria.fr/">OCaml</A>, ... are also OK). Starting point is |
|
52 the open source SAT-solver MiniSat (available <A HREF="http://minisat.se/Main.html">here</A>). |
|
53 The long-term hope is that your implementation becomes part of the interactive theorem prover |
|
54 <A HREF="http://www.cl.cam.ac.uk/research/hvg/isabelle/">Isabelle</A>.</p> |
|
55 |
|
56 <p> |
|
57 <B>Tasks:</B> Understand MiniSat, design and code a SAT-solver in ML, |
|
58 empirical evaluation and tuning of your code.</p> |
|
59 |
|
60 <p> |
|
61 <B>Literature:</B> A good starting point for reading about SAT-solving is the handbook |
|
62 article in <A HREF="http://www.cs.cornell.edu/gomes/papers/SATSolvers-KR-Handbook.pdf">here</A>. |
|
63 MiniSat is explained <A HREF="http://minisat.se/downloads/MiniSat.pdf">here</A> and |
|
64 <A HREF="http://minisat.se/Papers.html">here</A>. The standard reference for ML is |
|
65 <A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
|
66 of this book for the duration of the project). The best free implementation of ML is |
|
67 <A HREF="http://www.polyml.org/">PolyML</A>. |
|
68 </p> |
|
69 |
|
70 <li> <H4>[CU2] A Compiler for System F</H4> |
|
71 |
|
72 <p><b>Description:</b> |
|
73 <A HREF="http://en.wikipedia.org/wiki/System_F">System F</A> is a mini programming language, |
|
74 which is often used to study the theory behind programming languages, but is also used as |
|
75 a core-language of functional programming languages (for example |
|
76 <A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>). The language is small |
|
77 enough to implement in a reasonable amount of time a compiler to an |
|
78 idealised assembly language (preferably |
|
79 <A HREF="http://en.wikipedia.org/wiki/Typed_assembly_language">TAL</A>) or an abstract machine. |
|
80 This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette |
|
81 (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> |
|
82 as his implementation language. Other choices are of course possible. |
|
83 </p> |
|
84 |
|
85 <p> |
|
86 <b>Tasks:</b> |
|
87 Read the relevant literature and implement the various components of a compiler |
|
88 (parser, intermediate languages, simulator for the idealised assembly language). |
|
89 This project is for a good student with an interest in programming languages, |
|
90 who can also translate abstract ideas into code. If it is too difficult, the project can |
|
91 easily be scaled back to the |
|
92 <A HREF="http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus">simply-typed |
|
93 lambda calculus</A> (which is simpler than |
|
94 System F) or only some components of the compiler are implemented. |
|
95 </p> |
|
96 |
|
97 <p> |
|
98 <B>Literature:</B> |
|
99 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 |
|
100 paper about this subject is available <A HREF="http://www.iro.umontreal.ca/~monnier/icfp08.pdf">here</A>. |
|
101 A good starting point for TAL is <A HREF="http://www.cs.cornell.edu/talc/papers/tal-tr.pdf">here</A>. |
|
102 There is a lot of literature about compilers |
|
103 (for example <A HREF="http://www.cs.princeton.edu/~appel/papers/cwc.html">this book</A> - |
|
104 I can lend you my copy for the duration of the project). |
|
105 </p> |
|
106 |
|
107 <li> <H4>[CU3] Sorting Suffixes</H4> |
|
108 |
|
109 <p><b>Description:</b> Given a string, take all its suffixes, and sort them. |
|
110 This is often also called <A HREF="http://en.wikipedia.org/wiki/Suffix_array">suffix |
|
111 array sorting</A>. It sound simple, but there are some difficulties. |
|
112 The naive algorithm would generate all (suffix) strings and sort them |
|
113 using a standard sorting algorithm, for example quick-sort. Unfortunately, |
|
114 this algorithm is not optimal (it does not take into account that you sort |
|
115 suffixes) and it also takes an quadratic amount of space, which is a |
|
116 problem if you have to sort strings of several Mega-Bytes or even Giga-Bytes |
|
117 (happens often in biotech DNA information.<p> |
|
118 |
|
119 Aim: the notion of index on a text is central in many methods for text |
|
120 processing and for the management of textual databases. Suffix Arrays is one |
|
121 of these methods based on the sorted list of suffixes of the input text. The |
|
122 project consists in implementing a linear-time sorting algorithm and other |
|
123 elements related to Suffix Array construction and to Burrows-Wheeler text |
|
124 compression. Plan: study of the sorting problem in the literature starting |
|
125 with the reference below. Implementation of the sorting algorithm and the |
|
126 LCP computation to obtain a Suffix Array construction software. Then, using |
|
127 this work, implementation of the algorithms described in the second |
|
128 reference below. Deliverables: report, suffix sorting and associated |
|
129 software and their documentation. |
|
130 |
|
131 References: |
|
132 J. Kärkkäinen and P. Sanders, Simple linear work suffix array construction, in ICALP'03, LNCS 2719, Spinger, 2003, pp. 943--955. |
|
133 M. Crochemore, J. Désarménien and D. Perrin, A note on the Burrows-Wheeler transformation, Theoret. Comput. Sci., 2005, to appear. |
|
134 |
|
135 There is a horrendously complicated algorithm for solving these problems. |
|
136 Your task would be to understand it, and then implement it. |
|
137 |
|
138 <li> <H5>[CU 4] Simplification modulo Equivalences in Isabelle</H5> |
|
139 In this project you have to extend the simplifier of the Isabelle theorem |
|
140 prover. Currently, the simplifier only rewrites terms according to equalities |
|
141 l = r. Provided ~ is an equivalence relation, the simplifier should also |
|
142 be able to rewrite terms according to equivalences of the form l ~ r. |
|
143 This project requires knowledge of the functional programming language ML. |
|
144 |
|
145 <li><h5>[CU 5] Parsing with Derivatives</h5> |
|
146 |
|
147 Derivatives can be used to implement a regular expression matcher. In |
|
148 this project you have to apply this technique to parsing. The starting |
|
149 point for this project is the paper "Yacc is Dead" by Matthew Might. |
|
150 |
|
151 <li> <H5>[CU 6] Equivalence Checking of Regular Expression using Antimirov's Method<H5> |
|
152 |
|
153 </ul> |
|
154 </TD> |
|
155 </TR> |
|
156 </TABLE> |
|
157 |
|
158 <P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 --> |
|
159 <!-- hhmts start --> |
|
160 Last modified: Thu Dec 1 18:10:37 GMT 2011 |
|
161 <!-- hhmts end --> |
|
162 <a href="http://validator.w3.org/check/referer">[Validate this page.]</a> |
|
163 </BODY> |
|
164 </HTML> |