  Each Boolean function can be computed by a single-pass instruction sequence
that contains only instructions to set and get the content of Boolean
registers, forward jump instructions, and a termination instruction. Auxiliary
Boolean registers are not necessary for this. In the current paper, we show
that, in the case of the parity functions, shorter instruction sequences are
possible with the use of an auxiliary Boolean register in the presence of
instructions to complement the content of auxiliary Boolean registers. This
result supports, in a setting where programs are instruction sequences acting
on Boolean registers, a basic intuition behind the storage of auxiliary data,
namely the intuition that this makes possible a reduction of the size of a
program.
