On the contribution of backward jumps to instruction sequence expressiveness

TL;DR

This paper examines the role of backward jumps in instruction sequences, showing they are unnecessary for computability but crucial for controlling program length in sequential programming models.

Contribution

It clarifies the conditions under which backward jumps are essential, highlighting their importance in limiting program length rather than in computational expressiveness.

Findings

Backward jumps are superfluous for computability of Boolean functions.

Backward jumps prevent exponential growth in program length.

The study distinguishes between expressiveness and program size control.

Abstract

We investigate the expressiveness of backward jumps in a framework of formalized sequential programming called program algebra. We show that - if expressiveness is measured in terms of the computability of partial Boolean functions - then backward jumps are superfluous. If we, however, want to prevent explosion of the length of programs, then backward jumps are essential.