Program algebra for random access machine programs

TL;DR

This paper develops an algebraic framework for RAM programs, enabling equational reasoning about their computational behavior and complexity, and introduces a semi-realistic RAM model with a bit-oriented time measure.

Contribution

It introduces a novel algebraic theory for RAM instruction sequences, allowing formal reasoning about computation and complexity beyond traditional RAM models.

Findings

RAM programs can be analyzed algebraically

Semi-realistic RAMs are simulatable by Turing machines with quadratic overhead

A bit-oriented time complexity measure is proposed

Abstract

This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such behaviours and RAM memories. This theory provides a setting for the development of theory in areas such as computational complexity and analysis of algorithms that distinguishes itself by offering the possibility of equational reasoning to establish whether an instruction sequence computes a given function and being more general than the setting provided by any known version of the RAM model of computation. In this setting, a semi-realistic version of the RAM model of computation and a bit-oriented time complexity measure for this version are introduced. Under the time measure concerned, semi-realistic RAMs can be simulated by multi-tape Turing machines with quadratic time overhead.