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[CU1] Implementing a SAT-Solver in a Functional Programming Language
-
- Description:
- SAT-solver search for satisfying assignments of boolean formulas. Although this
- is a computationally hard problem (NP-complete),
- modern SAT-solvers routinely solve boolean formulas with 100,000 and more variables.
- Application areas of SAT-solver are manifold: they range from hardware verification to
- Sudoku solvers (see here).
- Every 2 years there is a competition of the best SAT-solvers in the world.
-
-
- Most SAT-solvers are written in C. The aim of this project is to design and implement
- a SAT-solver in a functional programming language (preferably
- ML, but
- Haskell,
- Scala,
- OCaml, ... are also OK). Starting point is
- the open source SAT-solver MiniSat (available here).
- The long-term hope is that your implementation becomes part of the interactive theorem prover
- Isabelle. For this
- the SAT-solver needs to be implemented in ML.
-
-
- Tasks: Understand MiniSat, design and code a SAT-solver in ML,
- empirical evaluation and tuning of your code.
-
-
- Literature: A good starting point for reading about SAT-solving is the handbook
- article here.
- MiniSat is explained here and
- here. The standard reference for ML is
- here (I can lend you my copy
- of this book for the duration of the project). The best free implementation of ML is
- PolyML.
-
-
- -
[CU2] A Compiler for System F
-
- Description:
- System F is a mini programming language,
- which is often used to study the theory behind programming languages, but is also used as
- a core-language of functional programming languages (for example
- Haskell). The language is small
- enough to implement in a reasonable amount of time a compiler to an
- idealised assembly language (preferably
- TAL) or an abstract machine.
- This has been explained in full detail in a PhD-thesis by Louis-Julien Guillemette
- (available in English here). He used Haskell
- as his implementation language. Other choices are possible.
-
-
-
- Tasks:
- Read the relevant literature and implement the various components of a compiler
- (parser, intermediate languages, simulator for the idealised assembly language).
- This project is for a good student with an interest in programming languages,
- who can also translate abstract ideas into code. If it is too difficult, the project can
- be easily scaled down to the
- simply-typed
- lambda calculus (which is simpler than
- System F) or to cover only some components of the compiler.
-
-
-
- Literature:
- The PhD-thesis by Louis-Julien Guillemette is required reading. A shorter
- paper about this subject is available here.
- A good starting point for TAL is here.
- There is a lot of literature about compilers
- (for example this book -
- I can lend you my copy for the duration of the project). A very good overview article
- about implementing compilers by
- Laurie Tratt is
- here.
-
-
- -
[CU3] Sorting Suffixes
-
- Description: Given a string, take all its suffixes, and sort them.
- This is often called suffix
- array sorting. It sound simple, but there are some difficulties.
- The naive algorithm would generate all suffix strings and sort them
- using a standard sorting algorithm, for example
- quicksort.
- The problem is that
- this algorithm is not optimal for suffix sorting: it does not take into account that you sort
- suffixes and it also takes a quadratic amount of space. This is a
- huge problem if you have to sort strings of several Megabytes or even Gigabytes,
- as happens often in biotech and DNA data mining. Suffix sorting is also a crucial operation for the
- Burrows-Wheeler transform
- on which the data compression algorithm of the popular
- bzip2
- program is based.
-
-
-
- There are more efficient algorithms for suffix sorting, for example
- here and
- here.
- However the most space efficient algorithm for suffix sorting
- (here)
- is horrendously complicated. Your task would be to understand it, and then implement it.
-
-
-
- Tasks:
- Start by reading the literature about suffix sorting. Then work through the
- 12-page paper
- explaining the horrendously complicated algorithm and implement it.
- Time permitting the work can include an implementation of the Burrows-Wheeler
- data compression. This project is for a good student, who likes to study in-depth
- algorithms. The project can be carried out in almost all programming languages,
- including C, Java, Scala, ML, Haskell and so on.
-
-
-
- Literature: A good starting point for reading about suffix sorting is the
- book by Crochemore.
- Another good introduction is
- here,
- which gives also good pointers for why efficient suffix sorting
- is practically relevant.
- Two simple algorithms are described
- here. The main literature is the 12-page
- article about in-place
- suffix sorting. The Burrows-Wheeler data compression is described
- here.
-
-
- -
[CU4] Simplification with Equivalence Relations in the Isabelle Theorem Prover
-
- Description:
- In this project you have to extend the simplifier of the
- Isabelle theorem prover.
- The simplifier is an important reasoning tool of this theorem prover: it
- replaces a term by another term that can be proved to be equal to it. However,
- currently the simplifier only rewrites terms according to equalities.
- Assuming ≈ is an equivalence relation, the simplifier should also be able
- to rewrite terms according to ≈. Since equivalence relations occur
- frequently in automated reasoning, this extension would make the simplifier
- more powerful and useful. The hope is that your code can go into the
- code base of Isabelle.
-
-
-
- Tasks:
- Read the paper
- about rewriting with equivalence relations. Get familiar with parts of the
- implementation of Isabelle (I will be of much help as I can). Implement
- the extension. This project is suitable for a student with a bit of math background.
- It requires knowledge of the functional programming language ML, which
- however can be learned quickly provided you have already written code
- in another functional programming language.
-
-
-
- Literature: A good starting point for reading about rewriting modulo equivalences
- is the paper here,
- which uses the ACL2 theorem prover. The implementation of the Isabelle theorem
- prover is described in much detail in this
- programming tutorial.
- The standard reference for ML is
- here (I can lend you my copy
- of this book for the duration of the project).
-
-
-
- [CU5] Lexing and Parsing with Derivatives
-
-
- Description:
- Lexing and parsing are usually done using automated tools, like
- lex and
- yacc. The problem
- with them is that they "work when they work", but if they do not, then they are
- black boxes
- which are difficult to debug and change. They are really quite
- clumsy to the point that Might and Darais wrote a paper titled
- "Yacc is dead".
-
-
- There is a simple algorithm for regular expression matching (that is lexing).
- This algorithm was introduced by
- Brzozowski
- in 1964. It is based on the notion of derivatives of regular expressions and
- has proved useful
- for practical lexing. Last year the notion of derivatives was extended by
- Might et al
- to context free grammars
- and parsing.
-
-
-
- Tasks: Get familiar with the two algorithms and implement them. Regular
- expression matching is relatively simple; parsing with derivatives is the
- harder part. Therefore you should empirically evaluate this part and
- tune your implementation. The project can be carried out in almost all programming
- languages, including C, Java, Scala, ML, Haskell and so on.
-
-
-
- Literature: This
- paper
- gives a modern introduction to derivative based lexing. Derivative-based
- parsing is explained here
- and here.
- A proposal for derivative PEG-parsing is
- here. The mailing
- list about PEGs is here.
-
-
--
[CU6] Equivalence Checking of Regular Expressions using the Method by Antimirov and Mosses
-
-
- Description:
- Solving the problem of deciding equivalence of regular expressions can be used
- to decide a number of problems in automated reasoning. Therefore one likes to
- have a method for equivalence checking that is as fast as possible. There have
- been a number of algorithms proposed in the past, but one based on a method
- by Antimirov and Mosses seems relatively simple and easy to implement.
-
-
-
- Tasks:
- The task is to implement the algorithm by Antimirov and Mosses and compare it to
- other methods. Hopefully the algorithm can be tuned to be faster than other
- methods. The project can be carried out in almost all programming languages, but
- as usual functional programming languages such Scala, ML, Haskell have an edge
- for this kind of problems.
-
-
-
- Literature:
- Central to this project are the papers here
- and here.
- Other methods have been described, for example,
- here.
- A relatively complicated method, based on automata, is described
- here.
-
-
- -
[CU7] Game-Playing Engine for Five-In-A-Row on a Large Board
-
-
- Literature:
- There is a web-page with various pointers to computer players
- here. There are
- also some good books about computer players, for example:
-
- | Artificial Intelligence: A Modern Approach by S. Russel and P. Norvig, Prentice Hall, 2003
- (a standard textbook about search strategies).
- |
- | Principles of Artificial Intelligence by N. J. Nilsson, Springer Verlag, 1980
- (a standard textbook about search strategies).
- |
-
- | Computer Game-Playing: Theory and Practice by M. Bramer, Ellis Horwood Ltd, 1983
- (considers techniques used for programming a variety of games: Chess, Go, Scrabble, Billiards,
- Othello, etc; includes theoretical issues about game searching).
- |
- | Chips Challenging Champions: Games, Computers and Artificial Intelligence by
- J. Schaeffer and H.J. van den Herik, North Holland, 2002.
- |
- |
- Artificial Intelligence for Games by I. Millington and J. Funge, Morgan Kaufmann, 2009.
- |
- |
- Computer Gamesmanship: The Complete Guide to Creating and Structuring Intelligent Games Programs
- by D.N.L. Levy, Simon and Schuster, 1983.
- |
-
-
-
- [CU8] Webserver for a Revision Control System
-
-
- Modern revision control systems are
- mercurial and
- git.
-
-
-
- Task: Build a webserver for a revision control system
- that allows user management.
-
-
-
-