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4 <TITLE>Christian Urban</TITLE> |
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31 <H2>2011/12 MSc Individual Projects</H2> |
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32 <H4>Supervisor: Christian Urban</H4> |
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33 <H4>Email: christian dot urban at kcl dot ac dot uk, Office: Strand Building S6.30</H4> |
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34 <H4>If you are interested in a project, please send me an email and we can discuss details. Please include |
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35 a short description about your programming skills and computer science background in your first email. |
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36 I will also need your King's username in order to book the project for you. Thanks.</H4> |
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37 |
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38 <ul class="striped"> |
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39 <li> <H4>[CU1] Implementing a SAT-Solver in a Functional Programming Language</H4> |
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40 |
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41 <p><B>Description:</b> |
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42 SAT-solver search for satisfying assignments of boolean formulas. Although this |
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43 is a computationally hard problem (<A HREF="http://en.wikipedia.org/wiki/NP-complete">NP-complete</A>), |
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44 modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables. |
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45 Application areas of SAT-solver are manifold: they range from hardware verification to |
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46 Sudoku solvers (see <a href="http://anytime.cs.umass.edu/aimath06/proceedings/P34.pdf">here</a>). |
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47 Every 2 years there is a competition of the best SAT-solvers in the world.</p> |
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48 |
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49 <p> |
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50 Most SAT-solvers are written in C. The aim of this project is to design and implement |
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51 a SAT-solver in a functional programming language (preferably |
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52 <A HREF="http://en.wikipedia.org/wiki/Standard_ML">ML</A>, but |
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53 <A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>, |
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54 <A HREF="http://www.scala-lang.org/">Scala</A>, |
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55 <A HREF="http://caml.inria.fr/">OCaml</A>, ... are also OK). Starting point is |
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56 the open source SAT-solver MiniSat (available <A HREF="http://minisat.se/Main.html">here</A>). |
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57 The long-term hope is that your implementation becomes part of the interactive theorem prover |
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58 <A HREF="http://www.cl.cam.ac.uk/research/hvg/isabelle/">Isabelle</A>. For this |
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59 the SAT-solver needs to be implemented in ML.</p> |
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60 |
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61 <p> |
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62 <B>Tasks:</B> Understand MiniSat, design and code a SAT-solver in ML, |
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63 empirical evaluation and tuning of your code.</p> |
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64 |
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65 <p> |
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66 <B>Literature:</B> A good starting point for reading about SAT-solving is the handbook |
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67 article <A HREF="http://www.cs.cornell.edu/gomes/papers/SATSolvers-KR-Handbook.pdf">here</A>. |
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68 MiniSat is explained <A HREF="http://minisat.se/downloads/MiniSat.pdf">here</A> and |
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69 <A HREF="http://minisat.se/Papers.html">here</A>. The standard reference for ML is |
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70 <A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
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71 of this book for the duration of the project). The best free implementation of ML is |
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72 <A HREF="http://www.polyml.org/">PolyML</A>. |
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73 </p> |
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74 |
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75 <li> <H4>[CU2] A Compiler for System F</H4> |
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76 |
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77 <p><b>Description:</b> |
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78 <A HREF="http://en.wikipedia.org/wiki/System_F">System F</A> is a mini programming language, |
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79 which is often used to study the theory behind programming languages, but is also used as |
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80 a core-language of functional programming languages (for example |
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81 <A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>). The language is small |
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82 enough to implement in a reasonable amount of time a compiler to an |
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83 idealised assembly language (preferably |
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84 <A HREF="http://en.wikipedia.org/wiki/Typed_assembly_language">TAL</A>) or an abstract machine. |
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85 This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette |
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86 (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> |
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87 as his implementation language. Other choices are possible. |
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88 </p> |
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89 |
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90 <p> |
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91 <b>Tasks:</b> |
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92 Read the relevant literature and implement the various components of a compiler |
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93 (parser, intermediate languages, simulator for the idealised assembly language). |
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94 This project is for a good student with an interest in programming languages, |
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95 who can also translate abstract ideas into code. If it is too difficult, the project can |
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96 be easily scaled down to the |
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97 <A HREF="http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus">simply-typed |
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98 lambda calculus</A> (which is simpler than |
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99 System F) or to cover only some components of the compiler. |
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100 </p> |
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101 |
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102 <p> |
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103 <B>Literature:</B> |
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104 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 |
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105 paper about this subject is available <A HREF="http://www.iro.umontreal.ca/~monnier/icfp08.pdf">here</A>. |
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106 A good starting point for TAL is <A HREF="http://www.cs.cornell.edu/talc/papers/tal-tr.pdf">here</A>. |
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107 There is a lot of literature about compilers |
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108 (for example <A HREF="http://www.cs.princeton.edu/~appel/papers/cwc.html">this book</A> - |
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109 I can lend you my copy for the duration of the project). A very good overview article |
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110 about implementing compilers by |
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111 <A HREF="http://tratt.net/laurie/">Laurie Tratt</A> is |
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112 <A HREF="http://tratt.net/laurie/tech_articles/articles/how_difficult_is_it_to_write_a_compiler">here</A>. |
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113 </p> |
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114 |
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115 <li> <H4>[CU3] Sorting Suffixes</H4> |
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116 |
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117 <p><b>Description:</b> Given a string, take all its suffixes, and sort them. |
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118 This is often called <A HREF="http://en.wikipedia.org/wiki/Suffix_array">suffix |
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119 array sorting</A>. It sound simple, but there are some difficulties. |
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120 The naive algorithm would generate all suffix strings and sort them |
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121 using a standard sorting algorithm, for example |
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122 <A HREF="http://en.wikipedia.org/wiki/Quicksort">quicksort</A>. |
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123 The problem is that |
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124 this algorithm is not optimal for suffix sorting: it does not take into account that you sort |
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125 suffixes and it also takes a quadratic amount of space. This is a |
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126 huge problem if you have to sort strings of several Megabytes or even Gigabytes, |
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127 as happens often in biotech and DNA data mining. Suffix sorting is also a crucial operation for the |
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128 <A HREF="http://en.wikipedia.org/wiki/Burrows-Wheeler_transform">Burrows-Wheeler transform</A> |
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129 on which the data compression algorithm of the popular |
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130 <A HREF="http://en.wikipedia.org/wiki/Bzip2">bzip2</A> |
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131 program is based. |
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132 </p> |
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133 |
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134 <p> |
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135 There are more efficient algorithms for suffix sorting, for example |
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136 <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 |
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137 <A HREF="http://ls11-www.cs.uni-dortmund.de/people/rahmann/teaching/ss2008/AlgorithmenAufSequenzen/09-walk-bwt.pdf">here</A>. |
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138 However the most space efficient algorithm for suffix sorting |
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139 (<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">here</A>) |
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140 is horrendously complicated. Your task would be to understand it, and then implement it. |
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141 </p> |
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142 |
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143 <p> |
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144 <B>Tasks:</B> |
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145 Start by reading the literature about suffix sorting. Then work through the |
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146 12-page <A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">paper</A> |
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147 explaining the horrendously complicated algorithm and implement it. |
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148 Time permitting the work can include an implementation of the Burrows-Wheeler |
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149 data compression. This project is for a good student, who likes to study in-depth |
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150 algorithms. The project can be carried out in almost all programming languages, |
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151 including C, Java, Scala, ML, Haskell and so on. |
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152 </p> |
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153 |
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154 <p> |
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155 <B>Literature:</B> A good starting point for reading about suffix sorting is the |
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156 <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. |
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157 Another good introduction is |
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158 <A HREF="http://people.unipmn.it/manzini/papers/esa02.pdf">here</A>, |
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159 which gives also good pointers for why efficient suffix sorting |
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160 is practically relevant. |
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161 Two simple algorithms are described |
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162 <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 |
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163 <A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">article</A> about in-place |
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164 suffix sorting. The Burrows-Wheeler data compression is described |
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165 <A HREF="http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pdf">here</A>. |
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166 </p> |
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167 |
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168 <li> <H4>[CU4] Simplification with Equivalence Relations in the Isabelle Theorem Prover</H4> |
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169 <p> |
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170 <B>Description:</B> |
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171 In this project you have to extend the simplifier of the |
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172 <A HREF="http://isabelle.in.tum.de/">Isabelle theorem prover</A>. |
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173 The simplifier is an important reasoning tool of this theorem prover: it |
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174 replaces a term by another term that can be proved to be equal to it. However, |
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175 currently the simplifier only rewrites terms according to equalities. |
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176 Assuming ≈ is an equivalence relation, the simplifier should also be able |
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177 to rewrite terms according to ≈. Since equivalence relations occur |
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178 frequently in automated reasoning, this extension would make the simplifier |
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179 more powerful and useful. The hope is that your code can go into the |
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180 code base of Isabelle. |
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181 </p> |
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182 |
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183 <p> |
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184 <B>Tasks:</B> |
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185 Read the <A HREF="http://www.springerlink.com/content/x7041m1807738832/">paper</A> |
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186 about rewriting with equivalence relations. Get familiar with parts of the |
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187 implementation of Isabelle (I will be of much help as I can). Implement |
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188 the extension. This project is suitable for a student with a bit of math background. |
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189 It requires knowledge of the functional programming language ML, which |
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190 however can be learned quickly provided you have already written code |
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191 in another functional programming language. |
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192 </p> |
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193 |
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194 <p> |
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195 <B>Literature:</B> A good starting point for reading about rewriting modulo equivalences |
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196 is the paper <A HREF="http://www.springerlink.com/content/x7041m1807738832/">here</A>, |
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197 which uses the ACL2 theorem prover. The implementation of the Isabelle theorem |
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198 prover is described in much detail in this |
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199 <A HREF="http://www.inf.kcl.ac.uk/staff/urbanc/Cookbook/">programming tutorial</A>. |
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200 The standard reference for ML is |
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201 <A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
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202 of this book for the duration of the project). |
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203 </p> |
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204 |
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205 |
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206 <li><h4>[CU5] Lexing and Parsing with Derivatives</h4> |
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207 |
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208 <p> |
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209 <B>Description:</B> |
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210 Lexing and parsing are usually done using automated tools, like |
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211 <A HREF="http://en.wikipedia.org/wiki/Lex_programming_tool">lex</A> and |
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212 <A HREF="http://en.wikipedia.org/wiki/Yacc">yacc</A>. The problem |
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213 with them is that they "work when they work", but if they do not, then they are |
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214 <A HREF="http://en.wikipedia.org/wiki/Black_box">black boxes</A> |
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215 which are difficult to debug and change. They are really quite |
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216 clumsy to the point that Might and Darais wrote a paper titled |
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217 "<A HREF="http://arxiv.org/pdf/1010.5023v1">Yacc is dead</A>".</p> |
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218 |
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219 <p> |
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220 There is a simple algorithm for regular expression matching (that is lexing). |
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221 This algorithm was introduced by |
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222 <A HREF="http://en.wikipedia.org/wiki/Janusz_Brzozowski_(computer_scientist)">Brzozowski</A> |
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223 in 1964. It is based on the notion of derivatives of regular expressions and |
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224 has proved <A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">useful</A> |
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225 for practical lexing. Last year the notion of derivatives was extended by |
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226 <A HREF="http://matt.might.net/papers/might2011derivatives.pdf">Might et al</A> |
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227 to <A HREF="http://en.wikipedia.org/wiki/Context-free_grammar">context free grammars</A> |
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228 and parsing. |
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229 </p> |
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230 |
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231 <p> |
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232 <B>Tasks:</B> Get familiar with the two algorithms and implement them. Regular |
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233 expression matching is relatively simple; parsing with derivatives is the |
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234 harder part. Therefore you should empirically evaluate this part and |
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235 tune your implementation. The project can be carried out in almost all programming |
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236 languages, including C, Java, Scala, ML, Haskell and so on. |
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237 </p> |
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238 |
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239 <p> |
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240 <B>Literature:</B> This |
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241 <A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">paper</A> |
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242 gives a modern introduction to derivative based lexing. Derivative-based |
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243 parsing is explained <A HREF="http://arxiv.org/pdf/1010.5023v1">here</A> |
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244 and <A HREF="http://matt.might.net/papers/might2011derivatives.pdf">here</A>. |
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245 A proposal for derivative PEG-parsing is |
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246 <A HREF="http://fmota.eu/2011/01/07/PEG-derivatives.html">here</a>. The mailing |
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247 list about PEGs is <A HREF="https://lists.csail.mit.edu/pipermail/peg/">here</A>. |
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248 </p> |
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249 |
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250 <li> <H4>[CU6] Equivalence Checking of Regular Expressions using the Method by Antimirov and Mosses</H4> |
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251 |
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252 <p> |
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253 <B>Description:</B> |
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254 Solving the problem of deciding equivalence of regular expressions can be used |
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255 to decide a number of problems in automated reasoning. Therefore one likes to |
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256 have a method for equivalence checking that is as fast as possible. There have |
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257 been a number of algorithms proposed in the past, but one based on a method |
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258 by Antimirov and Mosses seems relatively simple and easy to implement. |
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259 </p> |
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260 |
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261 <p> |
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262 <B>Tasks:</B> |
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263 The task is to implement the algorithm by Antimirov and Mosses and compare it to |
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264 other methods. Hopefully the algorithm can be tuned to be faster than other |
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265 methods. The project can be carried out in almost all programming languages, but |
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266 as usual functional programming languages such Scala, ML, Haskell have an edge |
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267 for this kind of problems. |
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268 </p> |
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269 |
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270 <p> |
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271 <B>Literature:</B> |
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272 Central to this project are the papers <A HREF="http://www.dcc.fc.up.pt/~nam/publica/ijcs08.pdf">here</A> |
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273 and <A HREF="http://www.dcc.fc.up.pt/~nam/publica/51480046.pdf">here</A>. |
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274 Other methods have been described, for example, |
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275 <A HREF="http://www4.informatik.tu-muenchen.de/~krauss/papers/rexp.pdf">here</A>. |
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276 A relatively complicated method, based on automata, is described |
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277 <A HREF="http://sardes.inrialpes.fr/~braibant/atbr/">here</A>. |
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278 </p> |
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279 |
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280 <li> <H4>[CU7] Game-Playing Engine for Five-In-A-Row on a Large Board</H4> |
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281 |
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282 <p> |
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283 <B>Literature:</b> |
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284 There is a web-page with various pointers to computer players |
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285 <A HREF="http://webdocs.cs.ualberta.ca/~games/">here</A>. There are |
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286 also some good books about computer players, for example: |
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287 <table cellspacing="10"> |
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288 <tr><td><i>Artificial Intelligence: A Modern Approach</i> by S. Russel and P. Norvig, Prentice Hall, 2003 |
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289 (a standard textbook about search strategies). |
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290 </td></tr> |
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291 <tr><td><i>Principles of Artificial Intelligence</i> by N. J. Nilsson, Springer Verlag, 1980 |
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292 (a standard textbook about search strategies). |
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293 </td></tr> |
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294 |
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295 <tr><td><i>Computer Game-Playing: Theory and Practice</i> by M. Bramer, Ellis Horwood Ltd, 1983 |
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296 (considers techniques used for programming a variety of games: Chess, Go, Scrabble, Billiards, |
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297 Othello, etc; includes theoretical issues about game searching). |
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298 </td></tr> |
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299 <tr><td><i>Chips Challenging Champions: Games, Computers and Artificial Intelligence</i> by |
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300 J. Schaeffer and H.J. van den Herik, North Holland, 2002. |
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301 </td></tr> |
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302 <tr><td> |
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303 <i>Artificial Intelligence for Games</i> by I. Millington and J. Funge, Morgan Kaufmann, 2009. |
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304 </td></tr> |
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305 <tr><td> |
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306 <i>Computer Gamesmanship: The Complete Guide to Creating and Structuring Intelligent Games Programs</i> |
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307 by D.N.L. Levy, Simon and Schuster, 1983. |
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308 </td></tr> |
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309 </table> |
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310 </p> |
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311 |
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312 <li><h4>[CU8] Webserver for a Revision Control System</h4> |
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313 |
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314 <p> |
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315 Modern revision control systems are |
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316 <A HREF="http://mercurial.selenic.com/">mercurial</A> and |
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317 <A HREF="http://git-scm.com/">git</A>. |
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318 </p> |
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319 |
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320 <p> |
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321 <b>Task:</b> Build a webserver for a revision control system |
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322 that allows user management. |
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323 </p> |
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324 |
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325 </ul> |
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326 </TD> |
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327 </TR> |
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328 </TABLE> |
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