I am a researcher in

I am a member of King's College.

### Contact

I can best be reached by email:**tcs27 [at] cam . ac . uk**

I am a researcher in

I am a member of King's College.

Most of the world's digital data is currently encoded in a
sequential form, and compression methods for sequences have
been studied extensively. However, there are many types of
non-sequential data for which good compression techniques are
still largely unexplored. This paper contributes insights and
concrete techniques for compressing various kinds of
non-sequential data via arithmetic coding, and derives
re-usable probabilistic data models from fairly generic
structural assumptions. Near-optimal compression methods are
described for certain types of permutations, combinations and
multisets; and the conditions for optimality are made explicit
for each method.

This article makes several improvements to the classic PPM algorithm,
resulting in a new algorithm with superior compression effectiveness
on human text. The key differences of our algorithm to classic PPM are
that: Ⓐ rather than the original escape mechanism, we use a
generalised blending method with explicit hyper-parameters that
control the way symbol counts are combined to form predictions;
Ⓑ different hyper-parameters are used for classes of different contexts;
and Ⓒ these hyper-parameters are updated dynamically using gradient
information. The resulting algorithm (PPM-DP) compresses human text
better than all currently published variants of PPM, CTW, DMC, LZ, CSE
and BWT, with runtime only slightly slower than classic PPM.

This article describes lossless compression algorithms for multisets
of sequences, taking advantage of the multiset's unordered structure.
Multisets are a generalisation of sets where members are allowed to
occur multiple times. A multiset can be encoded naïvely by simply
storing its elements in some sequential order, but then information is
wasted on the ordering. We propose a technique that transforms the
multiset into an order-invariant tree representation, and derive an
arithmetic code that optimally compresses the tree. Our method
achieves compression even if the sequences in the multiset are
individually incompressible (such as cryptographic hash sums). The
algorithm is demonstrated practically by compressing collections of
SHA-1 hash sums, and multisets of arbitrary, individually encodable
objects.

This thesis makes several contributions to the field of data
compression.
Compression algorithms are derived for a variety of
applications, employing
probabilistic modelling, Bayesian inference, and arithmetic coding;
and making the underlying probability distributions explicit
throughout.
A general compression toolbox is described, consisting of
practical algorithms for compressing data distributed by various
fundamental probability distributions, and mechanisms for combining
these algorithms in a principled way.
New mathematical theory is introduced for compressing objects
with an underlying combinatorial structure, such as permutations,
combinations, and multisets.
For text compression, a novel unifying construction is developed for a
family of context-sensitive compression algorithms, special cases of
which include the PPM algorithm and the Sequence Memoizer.
The work concludes with experimental results, example applications,
and a brief discussion on cost-sensitive compression and
adversarial sequences.

The Boolean Satisfiability Problem (SAT) belongs to the class of
NP-complete problems, meaning that there is no known deterministic
algorithm that can solve an arbitrary problem instance in less than
exponential time (parametrized on the length of the input). There is
great industrial demand for solving SAT, motivating the need for
algorithms which perform well. I present a comparison of two
approaches for solving SAT instances: DPLL (an exact algorithm from
classical computer science) and Survey Propagation (a probabilistic
algorithm from statistical physics). The two algorithms were compared
on randomly generated 3-SAT problems with varying clause to variable
ratios.

This dissertation outlines the the design of a statically typed
programming language for quantum computers,
and describes a working implementation of it
for classical computer systems.

I have taught various undergraduate courses at Cambridge University,
including:
*Probability Theory,
Types,
Artificial Intelligence,
Computation Theory,
Functional Programming,
Quantum Computation,
ML, Prolog, Java,*
and *Foundations of Computer Science*.

I also supervised a few undergraduate B.A. dissertations.

If you need sudokus in large quantities or with special properties, contact me! :)

(PS. The online version is basically working, but still in stealth mode. If you would like to have a preview before its official release, email me.)

PS: Many known functions will be detected if you build and click them, e.g. those of other combinators, Church numerals, tuples, lists, basic arithmetic operations, etc.

(An optional alternative for Unix/Linux-based systems: shell script rlogic.sh, which fetches and runs the latest version of the software straight from the internet.)

There's a diagram (PDF)/(PS) providing a graphical view of what

Please submit additions or corrections, so they can be included in the next version.

Read more (or just download the floppy image).