Max Gadouleau
Durham
Title: Computing without memory
Abstract: An elementary problem when writing a computer program is how
to swap the contents of two variables. Although the typical approach
consists of using a buffer, this operation can actually be performed
using XOR without memory. In this talk, we generalise this approach and
thus introduce a novel combinatorial framework for procedural
programming languages, where programs are allowed to update only one
variable at a time without the use of any additional memory. After
proving that any function can be computed in this fashion, we give some
results on the shortest length of a program computing a given function.
We then show that binary operations are not sufficient to compute any
function. If time permits, we finally investigate how using memory can
also be incorporated in our framework.