Formalization of Distributed and Dynamic Resources Allocation Using Category Theory

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.