Linear Software Models: Key Ideas

TL;DR

Linear Software Models applies linear algebra to develop a mathematical theory of software systems, emphasizing the Modularity Matrix as a key structure for understanding and designing modular software.

Contribution

This paper consolidates the core ideas of Linear Software Models, introducing the Modularity Matrix as a central algebraic tool for software analysis and design.

Findings

Modularity Matrix is central to the theory

Standard Modularity Matrix enables system comparison

High sparsity indicates high cohesion in software systems

Abstract

Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one was lacking a single source for its key ideas. This paper concisely distills foundational ideas and results obtained within Linear Software Models. First and foremost we claim that one must have a deep comprehension of the theory of software - the aim of this effort - before embarking into theory and practice of software engineering. The Modularity Matrix is the central algebraic structure of the software theory: it is the source of quantitative modularity criteria; it displays high cohesion, i.e. high sparsity; a Standard Modularity Matrix is defined - square and block-diagonal - enabling designs comparison for any software systems in a Software Design Laboratory. It triggers formulation of novel open questions waiting for resolution.