[Paper Review] On the definition of a theoretical concept of an operating system

J.A. Bergstra, C.A. Middelburg|arXiv (Cornell University)|Jun 4, 2010

Computability, Logic, AI Algorithms16 references3 citations

TL;DR

This paper proposes a formal, theoretical definition of an operating system as a central component within a stratified concept family grounded in program execution architectures and concurrency theory. It advocates for a bare, explicative definition rooted in program switch-over and interruption mechanisms, establishing a foundation for a unified mathematical theory of operating systems.

ABSTRACT

We dwell on how a definition of a theoretical concept of an operating system, suitable to be incorporated in a mathematical theory of operating systems, could look like. This is considered a valuable preparation for the development of a mathematical theory of operating systems.

Motivation & Objective

• Address the lack of a coherent theoretical foundation for operating systems in computer science despite decades of practical development.
• Identify that existing literature fails to provide rigorous definitions or theoretical frameworks for the concept of an operating system.
• Propose a formal, explicative definition of a theoretical concept of an operating system suitable for integration into a mathematical theory.
• Establish a conceptual framework based on analytic execution architectures and concurrency to underpin the definition.
• Lay the groundwork for a future mathematical theory of operating systems by defining core dependencies and hierarchical relationships among theoretical concepts.

Proposed method

• Use an elementary meta-theory of definitions to guide the construction of a formal, explicative definition of the theoretical concept of an operating system.
• Define the theoretical concept of an operating system as conceptually dependent on theoretical concepts of programs and analytic execution architectures.
• Formulate a stratified concept family definition where the operating system is the most central concept, with supporting definitions of programs and execution architectures.
• Base the concurrency model on an extension of existing concurrency theory (from [1]) to include program interruption and switch-over mechanisms.
• Ensure the definition is bare and formal, avoiding informal or pragmatic characterizations, to support mathematical rigor.
• Integrate utility and value measures as secondary concepts to support analysis within the theoretical framework.

Experimental results

Research questions

• RQ1 What constitutes a theoretically sound and mathematically rigorous definition of an operating system?
• RQ2 How can a theoretical concept of an operating system be formally defined in a way that connects to existing literature and practical systems?
• RQ3 What is the role of concurrency theory in modeling the behavior of operating systems?
• RQ4 How can a family of interrelated theoretical concepts (programs, execution architectures, OS) be structured hierarchically to support a coherent theory?
• RQ5 What meta-theoretical framework supports the definition of such a concept family in a way that enables formal analysis and utility evaluation?

Key findings

• A formal, bare definition of a theoretical concept of an operating system is both possible and necessary for the development of a mathematical theory of operating systems.
• The theoretical concept of an operating system is best defined as a component within an analytic execution architecture that enables program execution switch-over and interruption, forming a basis for concurrency modeling.
• The concept is conceptually dependent on formalized notions of programs and execution architectures, forming a stratified concept family with the OS as the central concept.
• An extended concurrency theory—building on prior work—can serve as the foundational framework to model the dynamic behavior of operating systems.
• Existing literature lacks serious theoretical definitions of operating systems, with most explanations being informal or one-dimensional, justifying the need for this formalization.
• The proposed framework supports future utility and value analysis by allowing the extension of the concept family with measures of system performance or resource usage.