Complexity constant under variable renaming – a modest counter-example

Weyuker proposed that the complexity of a program is constant regardless of the names of the variables (Property 8). Actually, she acknowledges that variable names might be meaningful when trying to assess psychological complexity. Then, she says that this meaningfulness presumably varies with the individual programmer, and does not consider this further. Her property 8 then states the opposite, that variable names are not meaningful.

I see lots of room for mischief here, and give a short example with three syntactically identical program fragments.

Consider the following program fragment:

A = B * C;

D = B * E;

F = A – D;

Then consider this fragment:

GrossSale = Units * PricePerUnit;

GrossCost = Units * CostPerUnit;

GrossProfit = GrossSale – GrossProfit;

Now consider this fragment:

IOIOIOIOIOIOIO1OIOIOIOIOIO = IOIOIO1OIOIOIOIOIOIOIOIOIOIOIOIO * IOIOIOIOIOIOIOI0IOIOIOIOIOIOIOIO;

IOIOIOIOIOIOIOIOIO1OIOIOIO = IOIOIO1OIOIOIOIOIOIOIOIOIOIOIOIO * IOIOIOIOIOIOIOIOIOIOIOIOIOIOIOIO;

IOIOIOIOIOIOIOIOIOIOIOIOIO = IOIOIOIOIOIOIO1OIOIOIOIOIO - IOIOIOIOIOIOIOIOIO1OIOIOIO;

I claim that all three of these fragments perform the same computation, and that they are renamings of the each other. But, I think it’s intuitively obvious to the most casual observer that the psychological complexity is vastly different.

This website's first version is by Ryan Knowles and is maintained by Pat McGee.