| author | Christian Urban <urbanc@in.tum.de> |
| Fri, 02 Dec 2011 17:37:46 +0000 | |
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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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<H4>If you are interested in a project, please send me email and we can discuss details.</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>. For this |
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the SAT-solver needs to be implemented in ML.</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 <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 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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be easily scaled down 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 to cover only some components of the compiler. |
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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 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 |
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<A HREF="http://en.wikipedia.org/wiki/Quicksort">quicksort</A>. |
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The problem is that |
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this algorithm is not optimal for suffix sorting: it does not take into account that you sort |
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suffixes and it also takes a quadratic amount of space. This is a |
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huge problem if you have to sort strings of several Megabytes or even Gigabytes, |
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as happens often in biotech and DNA data mining. Suffix sorting is also a crucial operation for the |
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<A HREF="http://en.wikipedia.org/wiki/Burrows?Wheeler_transform">Burrows-Wheeler transform</A> |
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on which the data compression algorithm of the popular |
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<A HREF="http://en.wikipedia.org/wiki/Bzip2">bzip2</A> |
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program is based. |
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</p> |
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<p> |
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There are more efficient algorithms for suffix sorting, for example |
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<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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<A HREF="http://ls11-www.cs.uni-dortmund.de/people/rahmann/teaching/ss2008/AlgorithmenAufSequenzen/09-walk-bwt.pdf">here</A>. |
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However the most space efficient algorithm for suffix sorting |
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(<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">here</A>) |
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is horrendously complicated. Your task would be to understand it, and then implement it. |
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</p> |
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<p> |
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<B>Tasks:</B> |
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Start by reading the literature about suffix sorting. Then work through the |
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12-page <A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">paper</A> |
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explaining the horrendously complicated algorithm and implement it. |
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Time permitting the work can include an implementation of the Burrows-Wheeler |
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data compression. This project is for a good student, who likes to study in-depth |
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algorithms. The project can be carried out in almost all programming languages, |
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including C, Java, Scala, ML, Haskell and so on. |
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</p> |
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<p> |
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<B>Literature:</B> A good starting point for reading about suffix sorting is the |
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<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 |
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<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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<A HREF="http://www.cs.rutgers.edu/~muthu/fm072.pdf">article</A> about in-place |
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suffix sorting. The Burrows-Wheeler data compression is described |
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<A HREF="http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-124.pdf">here</A>. |
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</p> |
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<li> <H4>[CU4] Simplification with Equivalence Relations in the Isabelle Theorem Prover</H4> |
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<p> |
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<B>Description:</B> |
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In this project you have to extend the simplifier of the |
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<A HREF="http://isabelle.in.tum.de/">Isabelle theorem prover</A>. |
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The simplifier is an important reasoning tool of this theorem prover: it |
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replaces a term by another term that can be proved to be equal to it. However, |
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currently the simplifier only rewrites terms according to equalities. |
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Assuming ≈ is an equivalence relation, the simplifier should also be able |
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to rewrite terms according to ≈. Since equivalence relations occur |
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frequently in automated reasoning, this extension would make the simplifier |
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more powerful and useful. The hope is that your code can go into the |
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code base of Isabelle. |
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</p> |
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<p> |
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<B>Tasks:</B> |
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Read the <A HREF="http://www.springerlink.com/content/x7041m1807738832/">paper</A> |
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about rewriting with equivalence relations. Get familiar with parts of the |
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implementation of Isabelle (I will be of much help as I can). Implement |
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the extension. This project is suitable for a student with a bit of math background. |
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It requires knowledge of the functional programming language ML, which |
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however can be learned quickly provided you have already written code |
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in another functional programming language. |
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</p> |
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<p> |
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<B>Literature:</B> A good starting point for reading about rewriting modulo equivalences |
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is the paper <A HREF="http://www.springerlink.com/content/x7041m1807738832/">here</A>, |
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which uses the ACL2 theorem prover. The implementation of the Isabelle theorem |
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prover is described in much detail in this |
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<A HREF="http://www.inf.kcl.ac.uk/staff/urbanc/Cookbook/">programming tutorial</A>. |
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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). |
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</p> |
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<li><h4>[CU5] Lexing and Parsing with Derivatives</h4> |
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<p> |
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<B>Description:</B> |
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Lexing and parsing are usually done using automated tools, like |
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<A HREF="http://en.wikipedia.org/wiki/Lex_programming_tool">lex</A> and |
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<A HREF="http://en.wikipedia.org/wiki/Yacc">yacc</A>. The problem |
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with them is that they "work when they work", but if not, they are |
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<A HREF="http://en.wikipedia.org/wiki/Black_box">black boxes</A> |
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which are difficult to debug and change. They are really quite |
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clumsy, to the point that Might wrote a paper titled |
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"<A HREF="http://arxiv.org/pdf/1010.5023v1">Yacc is dead</A>".</p> |
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<p> |
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There is simple algorithm for regular expression matching (that is lexing). |
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This algorithm was introduced by |
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<A HREF="http://en.wikipedia.org/wiki/Janusz_Brzozowski_(computer_scientist)">Brzozowski</A> |
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in 1964. It is based on the notion of derivatives of regular expressions and |
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has proved <A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">useful</A> |
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for practical lexing. Last year the notion of derivatives was extended by |
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<A HREF="http://matt.might.net/papers/might2011derivatives.pdf">Might et al</A> |
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to <A HREF="http://en.wikipedia.org/wiki/Context-free_grammar">context free grammars</A> |
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and parsing. |
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</p> |
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<p> |
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<B>Tasks:</B> Get familiar with the two algorithms and implement them. Regular |
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expression matching is relatively simple; parsing with derivatives is the |
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harder part. Therefore you should empirically evaluate this part and |
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tune your implementation. The project can be carried out in almost all programming |
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languages, including C, Java, Scala, ML, Haskell and so on. |
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</p> |
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<p> |
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<B>Literature:</B> This |
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<A HREF="http://www.cl.cam.ac.uk/~so294/documents/jfp09.pdf">paper</A> |
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gives a modern introduction to derivative based lexing. Derivative-based |
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parsing is explained <A HREF="http://arxiv.org/pdf/1010.5023v1">here</A> |
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and <A HREF="http://matt.might.net/papers/might2011derivatives.pdf">here</A>. |
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</p> |
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<li> <H4>[CU6] Equivalence Checking of Regular Expressions using the Method by Antimirov and Mosses</H4> |
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<p> |
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<B>Description:</B> |
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Solving the problem of deciding equivalence of regular expressions can be used |
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to decide a number of problems in automated reasoning. Therefore one likes to |
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have a method for equivalence checking that is as fast as possible. |
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</p> |
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<p> |
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<B>Tasks:</B> |
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The task is to implement the algorithm by Antimirov and Mosses and compare it to |
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other methods. Hopefully the algorithm can be tuned to be faster than other |
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methods. |
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</p> |
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<p> |
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<B>Literature:</B> |
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Central to this project is the paper <A HREF="http://www.dcc.fc.up.pt/~nam/publica/ijcs08.pdf">here</A>. |
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Other methods have been described, for example, |
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<A HREF="http://www4.informatik.tu-muenchen.de/~krauss/papers/rexp.pdf">here</A>. |
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</p> |
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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: Fri Dec 2 03:26:32 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> |