+-
[CU1] Automata Minimisation
+
+ Description:
+ Deterministic finite automata
+ have many uses in Computer Science, for example for lexing
+ program code. In order to improve their run-time, automata need to be minimised, that
+ is transformed into equivalent automata with the smallest possible number of state
+ nodes.
+
+
+
+ There is a little known method for minimising deterministic finite
+ automata by
+ Janusz Brzozowski.
+ This method first reverses the edges of an automaton, which produces
+ a potentially non-deterministic automaton. The non-deterministic automaton is
+ then determinised using the usual powerset construction. This is repeated
+ once more and voila you obtain a minimised version of the automaton
+ you started with. It is rather surprising that this method works at all:
+ the powerset construction might produce an automaton with an exponentially
+ larger number of states, completely contrary to the idea of minimising the
+ number of states. The task of this project is to implement this method, check that
+ it actually works with some examples and
+ compare it with more traditional methods for automata minimisation
+ (in terms of run-time, code complexity, etc). Examples can be
+ obtained by translating regular expressions into automata.
+
+
+
+ Literature:
+ A good place to start with this project are the wikipedia articles
+ here and
+ here.
+ The authoritative book
+ on automata is by John Hopcroft and Jeffrey Ullmann (available in the library).
+ There is also an online course about automata by Ullman at
+ Coursera, though IMHO not
+ done with love. There
+ is also the book Automata and Computability by
+ Dexter Kozen including more
+ advanced material about automata.
+ Finally, there are millions of other pointers about automata
+ minimisation on the web.
+
+
+
+ Skills:
+ This is a project for a student with an interest in theory and some
+ reasonable programming skills. The project can be easily implemented
+ in languages like
+ Scala,
+ ML,
+ Haskell,
+ Python, etc.
+
+
+ -
[CU2] Equivalence Checking of Regular Expressions
+
+ Description:
+ Solving the problem of deciding the equivalence of regular expressions can be used
+ to decide a number of problems in automated reasoning. Recently,
+ Andreas Asperti
+ proposed a simple method for deciding regular expression equivalence described
+ here.
+ The task is to implement this method and test it on examples.
+ It would be also interesting to see whether Asperti's method also applies to
+ extended regular expressions, described
+ here.
+
+
+
+ Literature:
+ The central literature is obviously the papers
+ here and
+ here.
+ Asperti has also some slides here.
+ More references about regular expressions can be found
+ here.
+
+
+
+ Skills:
+ This is a project for a student with a passion for theory and some
+ reasonable programming skills. The project can be easily implemented
+ in languages like Scala
+ Scala,
+ ML,
+ Haskell,
+ Python, etc.
+ Being able to read Haskell
+ code is beneficial for the part involving extended regular expressions.
+
+
+ -
[CU3] Machine Code Generation for a Simple Compiler
+
+ Description:
+ Compilers translate high-level programs that humans can read and write into
+ efficient machine code that can be run on a CPU or virtual machine.
+ I recently implemented a very simple compiler for a very simple functional
+ programming language following this
+ paper
+ (also described here).
+ My code, written in Scala, of this compiler is
+ here.
+ The compiler can deal with simple programs involving natural numbers, such
+ as Fibonacci numbers
+ or factorial (but it can be easily extended - that is not the point).
+
+
+
+ While the hard work has been done (understanding the two papers above),
+ my compiler only produces some idealised machine code. For example I
+ assume there are infinitely many registers. The goal of this
+ project is to generate machine code which is more realistic and can
+ run on a CPU, like x86, or run on a virtual machine, say JVM.
+ This gives probably a speedup of thousand times in comparison to
+ my naive machine code and virtual machine. The project
+ requires to dig into the literature about real CPUs and generating
+ real machine code.
+
+
+
+ Literature:
+ 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.
+ An introduction into x86 machine code is here.
+ A simple assembler for the JVM is described here.
+ An interesting twist of this project is to not generate code for a CPU, but
+ for the intermediate language of the LLVM compiler
+ (also described here and
+ here).
+
+
+ Skills:
+ This is a project for a student with a deep interest in programming languages and
+ compilers. Since my compiler is implemented in Scala,
+ it would make sense to continue this project in this language. I can be
+ of help with questions and books about Scala.
+ But if Scala is a problem, my code can also be translated quickly into any other functional
+ language.
+
+
+ -
[CU4] Implementation of Register Spilling Algorithms
+
+ Description:
+ This project is similar to [CU3]. The emphasis here, however, is on the
+ implementation and comparison of register spilling algorithms, also often called register allocation
+ algorithms. They are part of any respectable compiler. As said
+ in [CU3], however, my simple compiler lacks them and assumes an infinite amount of registers instead.
+ Real CPUs however only provide a fixed amount of registers (for example
+ x86-64 has 16 general purpose registers). Whenever a program needs
+ to hold more values than registers, the values need to be “spilled”
+ into the main memory. Register spilling algorithms try to minimise
+ this spilling, since fetching values from main memory is a costly
+ operation.
+
+
+
+ The classic algorithm for register spilling uses a
+ graph-colouring method.
+ However, for some time the LLVM compiler
+ used a supposedly more efficient method, called the linear scan allocation method
+ (described
+ here).
+ However, it was later decided to abandon this method in favour of
+ a
+ greedy register allocation method. It would be nice if this project can find out
+ what the issues are with these methods and implement at least one of them for the
+ simple compiler referenced in [CU3].
+
+
+
+ Literature:
+ The graph colouring method is described in Andrew Appel's
+ book on compilers
+ (I can give you my copy of this book, if it is not available in the library).
+ There is also a survey
+ article
+ about register allocation algorithms with further pointers.
+
+
+ Skills:
+ Same skills as [CU3].
+
+
+ -
[CU5] A Student Polling System
+
+ Description:
+ One of the more annoying aspects of giving a lecture is to ask a question
+ to the students and no matter how easy the questions is to not
+ receive an answer. Recently, the online course system
+ Udacity made an art out of
+ asking questions during lectures (see for example the
+ Web Application Engineering
+ course CS253).
+ The lecturer there gives multiple-choice questions as part of the lecture and the students need to
+ click on the appropriate answer. This works very well in the online world.
+ For “real-world” lectures, the department has some
+ clickers
+ (these are little devices part of an audience response systems). However,
+ they are a logistic nightmare for the lecturer: they need to be distributed
+ during the lecture and collected at the end. Nowadays, where students
+ come with their own laptop or smartphone to lectures, this can
+ be improved.
+
+
+
+ The task of this project is to implement an online student
+ polling system. The lecturer should be able to prepare
+ questions beforehand (encoded as some web-form) and be able to
+ show them during the lecture. The students
+ can give their answers by clicking on the corresponding webpage.
+ The lecturer can then collect the responses online and evaluate them
+ immediately. Such a system is sometimes called
+ HTML voting.
+ There are a number of commercial
+ solutions for this problem, but they are not easy to use (in addition
+ to being ridiculously expensive). A good student can easily improve upon
+ what they provide.
+
+
+
+ The problem of student polling is not as hard as
+ electronic voting,
+ which essentially is still an unsolved problem in Computer Science. The
+ students only need to be prevented from answering question more than once thus skewing
+ any statistics. Unlike electronic voting, no audit trail needs to be kept
+ for student polling. Restricting the number of questions can probably be solved
+ by setting appropriate cookies on the students
+ computers or smart phones.
+
+
+
+ Literature:
+ The project requires fluency in a web-programming language (for example
+ Javascript,
+ PHP,
+ Java, Python, Go, Scala,
+ Ruby)
+ and possibly a cloud application platform (for example
+ Google App Engine or
+ Heroku).
+ For web-programming the
+ Web Application Engineering
+ course at Udacity is a good starting point
+ to be aware of the issues involved. This course uses Python.
+
+
+
+ Skills:
+ In order to provide convenience for the lecturer, this project needs very good web-programming skills. A
+ hacker mentality
+ (see above) is probably very beneficial: web-programming is an area that only emerged recently and
+ many tools still lack maturity. You probably have to experiment a lot with several different
+ languages and tools.
+
+
+
+