On instruction sets for Boolean registers in program algebra

TL;DR

This paper investigates the functional completeness of all possible instruction sets for Boolean registers within program algebra, aiming to better understand instruction sequence size complexity and its lower bounds.

Contribution

It provides a comprehensive analysis of instruction set size bounded functional completeness for Boolean registers, extending prior work in program algebra.

Findings

Identifies which instruction sets are size bounded functionally complete

Provides criteria for functional completeness of instruction sets

Enhances understanding of instruction sequence size complexity

Abstract

In previous work carried out in the setting of program algebra, including work in the area of instruction sequence size complexity, we chose instruction sets for Boolean registers that contain only instructions of a few of the possible kinds. In the current paper, we study instruction sequence size bounded functional completeness of all possible instruction sets for Boolean registers. We expect that the results of this study will turn out to be useful to adequately assess results of work that is concerned with lower bounds of instruction sequence size complexity.