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

In his doctoral research (DPhil thesis available 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!—is dealt with rigorously in the doctoral work).

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