On instruction sets for Boolean registers in program algebra

In program algebra, different instruction sets for Boolean registers are conceivable. In previous work on instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only a few of the possible instructions. In the current paper, we study instruction sequence size bounded functional completeness of instruction sets for Boolean registers. This work is among other things a requisite for making progress with proving lower bounds of non-asymptotic instruction sequence size complexity in cases where auxiliary Boolean registers may be used.