| author | Christian Urban <urbanc@in.tum.de> |
| Thu, 01 Dec 2011 23:36:19 +0000 | |
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<BASE HREF="http://www.inf.kcl.ac.uk/staff/urbanc/"> |
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RULES="all"> |
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VALIGN="TOP"> |
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<H2>2011/12 MSc Individual Projects</H2> |
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<H4>Supervisor: Christian Urban</H4> |
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<H4>Email: @kcl Office: Strand Building S6.30</H4> |
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<ul class="striped"> |
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<li> <H4>[CU1] Implementing a SAT-Solver in a Functional Programming Language</H4> |
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<p><B>Description:</b> |
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SAT-solver search for satisfying assignments of boolean formulas. Although this |
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is a computationally hard problem (<A HREF="http://en.wikipedia.org/wiki/NP-complete">NP-complete</A>), |
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modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables. |
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Application areas of SAT-solver are manifold: they range from hardware verification to |
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Sudoku solvers. Every 2 years there is a competition of the best SAT-solvers in the world.</p> |
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<p> |
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Most SAT-solvers are written in C. The aim of this project is to design and implement |
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a SAT-solver in a functional programming language (preferably |
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<A HREF="http://en.wikipedia.org/wiki/Standard_ML">ML</A>, but |
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<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>, |
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<A HREF="http://www.scala-lang.org/">Scala</A>, |
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<A HREF="http://caml.inria.fr/">OCaml</A>, ... are also OK). Starting point is |
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the open source SAT-solver MiniSat (available <A HREF="http://minisat.se/Main.html">here</A>). |
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The long-term hope is that your implementation becomes part of the interactive theorem prover |
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<A HREF="http://www.cl.cam.ac.uk/research/hvg/isabelle/">Isabelle</A>.</p> |
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<p> |
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<B>Tasks:</B> Understand MiniSat, design and code a SAT-solver in ML, |
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empirical evaluation and tuning of your code.</p> |
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<p> |
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<B>Literature:</B> A good starting point for reading about SAT-solving is the handbook |
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article in <A HREF="http://www.cs.cornell.edu/gomes/papers/SATSolvers-KR-Handbook.pdf">here</A>. |
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MiniSat is explained <A HREF="http://minisat.se/downloads/MiniSat.pdf">here</A> and |
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<A HREF="http://minisat.se/Papers.html">here</A>. The standard reference for ML is |
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<A HREF="http://www.cl.cam.ac.uk/~lp15/MLbook/">here</A> (I can lend you my copy |
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of this book for the duration of the project). The best free implementation of ML is |
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<A HREF="http://www.polyml.org/">PolyML</A>. |
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</p> |
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<li> <H4>[CU2] A Compiler for System F</H4> |
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<p><b>Description:</b> |
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<A HREF="http://en.wikipedia.org/wiki/System_F">System F</A> is a mini programming language, |
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which is often used to study the theory behind programming languages, but is also used as |
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a core-language of functional programming languages (for example |
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<A HREF="http://haskell.org/haskellwiki/Haskell">Haskell</A>). The language is small |
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enough to implement in a reasonable amount of time a compiler to an |
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idealised assembly language (preferably |
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<A HREF="http://en.wikipedia.org/wiki/Typed_assembly_language">TAL</A>) or an abstract machine. |
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This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette |
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(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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as his implementation language. Other choices are of course possible. |
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</p> |
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<p> |
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<b>Tasks:</b> |
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Read the relevant literature and implement the various components of a compiler |
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(parser, intermediate languages, simulator for the idealised assembly language). |
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This project is for a good student with an interest in programming languages, |
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who can also translate abstract ideas into code. If it is too difficult, the project can |
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easily be scaled back to the |
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<A HREF="http://en.wikipedia.org/wiki/Simply_typed_lambda_calculus">simply-typed |
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lambda calculus</A> (which is simpler than |
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System F) or only some components of the compiler are implemented. |
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</p> |
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<p> |
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<B>Literature:</B> |
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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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paper about this subject is available <A HREF="http://www.iro.umontreal.ca/~monnier/icfp08.pdf">here</A>. |
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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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There is a lot of literature about compilers |
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(for example <A HREF="http://www.cs.princeton.edu/~appel/papers/cwc.html">this book</A> - |
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I can lend you my copy for the duration of the project). |
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</p> |
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<li> <H4>[CU3] Sorting Suffixes</H4> |
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<p><b>Description:</b> Given a string, take all its suffixes, and sort them. |
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This is often also called <A HREF="http://en.wikipedia.org/wiki/Suffix_array">suffix |
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array sorting</A>. It sound simple, but there are some difficulties. |
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The naive algorithm would generate all (suffix) strings and sort them |
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using a standard sorting algorithm, for example quick-sort. Unfortunately, |
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this algorithm is not optimal (it does not take into account that you sort |
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suffixes) and it also takes an quadratic amount of space, which is a |
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problem if you have to sort strings of several Mega-Bytes or even Giga-Bytes |
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(happens often in biotech DNA information.<p> |
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Aim: the notion of index on a text is central in many methods for text |
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processing and for the management of textual databases. Suffix Arrays is one |
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of these methods based on the sorted list of suffixes of the input text. The |
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project consists in implementing a linear-time sorting algorithm and other |
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elements related to Suffix Array construction and to Burrows-Wheeler text |
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compression. Plan: study of the sorting problem in the literature starting |
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with the reference below. Implementation of the sorting algorithm and the |
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LCP computation to obtain a Suffix Array construction software. Then, using |
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this work, implementation of the algorithms described in the second |
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reference below. Deliverables: report, suffix sorting and associated |
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software and their documentation. |
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References: |
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J. Kärkkäinen and P. Sanders, Simple linear work suffix array construction, in ICALP'03, LNCS 2719, Spinger, 2003, pp. 943--955. |
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M. Crochemore, J. Désarménien and D. Perrin, A note on the Burrows-Wheeler transformation, Theoret. Comput. Sci., 2005, to appear. |
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There is a horrendously complicated algorithm for solving these problems. |
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Your task would be to understand it, and then implement it. |
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<li> <H5>[CU 4] Simplification modulo Equivalences in Isabelle</H5> |
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In this project you have to extend the simplifier of the Isabelle theorem |
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prover. Currently, the simplifier only rewrites terms according to equalities |
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l = r. Provided ~ is an equivalence relation, the simplifier should also |
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be able to rewrite terms according to equivalences of the form l ~ r. |
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This project requires knowledge of the functional programming language ML. |
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<li><h5>[CU 5] Parsing with Derivatives</h5> |
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Derivatives can be used to implement a regular expression matcher. In |
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this project you have to apply this technique to parsing. The starting |
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point for this project is the paper "Yacc is Dead" by Matthew Might. |
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<li> <H5>[CU 6] Equivalence Checking of Regular Expression using Antimirov's Method<H5> |
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</ul> |
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</TD> |
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</TR> |
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</TABLE> |
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<P><!-- Created: Tue Mar 4 00:23:25 GMT 1997 --> |
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<!-- hhmts start --> |
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Last modified: Thu Dec 1 18:10:37 GMT 2011 |
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<!-- hhmts end --> |
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<a href="http://validator.w3.org/check/referer">[Validate this page.]</a> |
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</BODY> |
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</HTML> |