Formalization of Distributed and Dynamic Resources Allocation Using Category Theory

Abstract

Distribution and dynamics are the main characteristics of resource allocation problem. Despite the variety of approaches and models proposed for the problem, a systematic formalization and a general solution strategy are missing. This paper takes a step towards this goal by proposing a categorical formalization of resource allocation, which not only represents both distributed and dynamic features, but also formally prove the properties of symmetry, safety(non-deadlock), liveness(non-starvation) and concurrency. The application to the wireless sensor networks demonstrates the practicability of our formal model and emphasizes the strengths of category theory-its simple theory, abstract mechanism, diagrammatical representation and its expressive power in representing and reasoning many concepts of computer science.

A Categorical Approach Towards Metamodeling Cyber-physical Systems

“…According to the three modeling steps, a possible direction can be to use a natural link between category theory and graph theory, which is frequently used to model sensor networks [26]. This approach has been used in [27], where the formalization of distributed and dynamic resources allocation problem for modeling wireless sensor networks has been presented via category theory. Thus, the next step is to extend existing results in modeling cyber-physical systems with graph theory towards a more formal description by category theory.…”