Categorial semantics of a solution to distributed dining philosophers problem

  • Authors:

  • Zhen You;Jinyun Xue;Shi Ying

  • Affiliations:

  • State Key Lab of Software Engineering, Wuhan University, Wuhan, Hubei Province, P.R.China and Provincial Key Laboratory for High-Performance Computing Technology, Jiangxi Normal University, Nancha ...;State Key Lab of Software Engineering, Wuhan University, Wuhan, Hubei Province, P.R.China and Provincial Key Laboratory for High-Performance Computing Technology, Jiangxi Normal University, Nancha ...;State Key Lab of Software Engineering, Wuhan University, Wuhan, Hubei Province, P.R.China

  • Venue:
  • FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
  • Year:
  • 2010

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Abstract

Distributed dining philosophers is regarded as one of the most representative resource allocation problems. Many strategies are employed for avoiding deadlock and starvation, the two well-known problems in Distributed Dining Philosophers Problem(DDPP). In this paper, the formal semantics of DDPP are originally proposed by using category theory based on the Chandy-Mirsa's acyclic directed graph strategy. The goal is to demonstrate how category theory is used in precisely defining categorical semantics and diagrammatically describing philosophers' priority, states-transition, and composition of processes, rather than to design a new algorithm to solve the DDPP. Compared with other formal techniques, category theory not only provides a good mathematical structure for formalizing different relationships and interactions at different abstract levels, but also its diagrammatical representation strengthens the traceability and understandability of philosophers' priority and states-transformation; additionally, its universal constructions (like colimit) offer the ability to manipulate and reason about system configuration.