  It is currently not possible to quantify the resources needed to perform a
computation. As a consequence, it is not possible to reliably evaluate the
hardware resources needed for the application of algorithms or the running of
programs. This is apparent in both computer science, for instance, in
cryptanalysis, and in neuroscience, for instance, comparative neuro-anatomy. A
System versus Environment game formalism is proposed based on Computability
Logic that allows to define a computational work function that describes the
theoretical and physical resources needed to perform any purely algorithmic
computation. Within this formalism, the cost of a computation is defined as the
sum of information storage over the steps of the computation. The size of the
computational device, eg, the action table of a Universal Turing Machine, the
number of transistors in silicon, or the number and complexity of synapses in a
neural net, is explicitly included in the computational cost. The proposed cost
function leads in a natural way to known computational trade-offs and can be
used to estimate the computational capacity of real silicon hardware and neural
nets. The theory is applied to a historical case of 56 bit DES key recovery, as
an example of application to cryptanalysis. Furthermore, the relative
computational capacities of human brain neurons and the C. elegans nervous
system are estimated as an example of application to neural nets.

Computational Complexity;Cryptography and Security