2015/10/15 by Iaakov Exman, Exman, Iaakov
Computer Science · Mathematics · #Advanced Software Engineering Methodologies #Algebra over a field #Cohesion (chemistry) #Computer science #D.2.2 #FOS: Computer and information sciences #Key (lock) #Mathematics #Modularity (biology) #Programming language #Pure mathematics #Service-Oriented Architecture and Web Services #Software #Software Engineering (cs.SE) #Software Engineering Research #Software construction #Software development #Software engineering #Theoretical computer science #cs.SE
paper · pdf · doi:10.48550/arxiv.1510.04652
26 pages, 4 figures
arxiv created 2015/10/15 · openalex publication_date 2015/10/15 · arxiv updated 2015/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.