Categorial Semantics of a Solution to Distributed Dining Philosophers Problem

Generalised Dining Philosophers as Feedback Control

“…You et al [38] solve the Distributed Dining Philosophers problem, which is the same as the Generalized Dining Philosophers problem, using category theory. The phases of philosophers, priority of philosophers, state-transitions etc.…”

Formalization of Distributed and Dynamic Resources Allocation Using Category Theory

“…This paper takes a step towards this goal by proposing a categorical formalization of resource allocation, which not only represents both dynamic and distributed aspects of the problem, but also formally prove the properties of symmetry, safety(nondeadlock), liveness(non-starvation) and concurrency. The formal models defined in the paper is based on Chandy-Misra's acyclic directed graph strategy [5,27] and our previous experience [28] in implementing the categorical semantics for distributed dinning philosophers problem. Finally, we describe how our categorical models can be implemented in wireless sensor networks.…”

Unified Categorical Models for Three Typical Resource Allocation Problems

“…Different from the other previous models, the paper presents an unified and efficient categorical-formalization for three typical resource allocation problems (including dinning philosophers problem, drinking philosophers problem and committee coordination problem) based on Chandy-Misra's acyclic directed graph strategy [3,4] and our previous experience [17] in implementing the categorical semantics for distributed dinning philosophers problem. The systematic categorical-models not only formalize usual concepts in resource allocation using categorical entities (such as objects, morphisms), but also give good directions to reason the relationships between these three problems.…”

“…Each philosopher requires a fixed subset of the resources and has to acquire all required resources for the philosopher to perform its Critical Section (CS), and every resource could be allocated to at most one philosopher at a time. According to our previous paper [17], the dinners category is detailedly defined. The dinners category D is composed of a objects collection Θ = {P 1 , P 1 , ..., P n }, each object represents a philosopher; and a morphisms collection Ψ, where for every morphism f ij : P i → P j ∈ Ψ (P i , P j ∈ Θ ∧ P i ̸ = P j ) means that philosopher P i has priority over its neighboring-philosopher P j , and for every object P i in Θ, there is an identity morphism id i : P i → P i , which indicates that the priority of philosopher P i is equivalent to itself.…”