Dr Blakey’s chief research interest is computational complexity, specifically as pertaining to unconventional computers.

In his doctoral research (DPhil thesis available here, and many associated papers, etc. here), he demonstrates that unconventional computers warrant unconventional complexity analysis, and accordingly introduces a computational-model-independent framework of complexity theory, based not only upon traditional computational resources (time and space) but also upon non-standard ones (precision, energy, etc.). From this framework arise corresponding complexity classes; the doctoral work includes proofs of theorems concerning the inclusions therebetween.

This doctoral work allows: insightful complexity analysis of unconventional computers; comparison of large, model-heterogeneous sets of computers, and correspondingly improved bounds upon the complexity of problems; assessment of novel, unconventional systems against existing, Turing-machine benchmarks; increased confidence in the difficulty of problems (and, hence, in the security of cryptographic systems); effective approaches to the resolution of existing disputes in the literature, and to various fundamental questions concerning the nature of computation; etc.

The work was motivated by consideration of an analogue computer (for which Blakey, during his time at IBM, filed a US patent) that factorizes numbers in polynomial time and space (the catch—for of course there is one!—concerns precision, and is dealt with rigorously in the doctoral work, using the framework introduced therein).

Aside from this primary interest in complexity theory, Blakey is also researching combinatorics (more specifically, certain number-theoretic aspects of graph colourings), and links between algorithms and biological sciences.

Blakey’s earlier research includes work on cellular-automatic implementations of communication channels (MSc dissertation available here, and associated, more recent conference paper here) and on applications of group theory and combinatorics to Rubik’s cube (BA extended essay available here).