On the Relativistic Structure of Logical Time in Distributed Systems 

In: Datation et Controle des Executions Reparties, Bigre 78 (ISSN 0221-525), 
pp. 3-20, 1992 

A distributed system, where processes communicate via messages with 
unpredictable transmission times, is characterized by the fact that no process 
has an up-to-date and consistent view of the system's global state. 
Furthermore, the notion of global time does not exist a priori within such a 
system. However, by defining time to be a partially ordered set of vectors 
forming a lattice structure, one gets a notion of logical time which is 
realizable in such a system and which represents the causality structure of 
events in an isomorphic way. With this definition, the relations "later" and 
"at the same time" get a new and generalized but adequate interpretation. 
Interestingly, it turns out that this notion of time is similar in structure 
to Minkowski's relativistic space-time model. We motivate the concept of 
"vector time", elaborate its properties, and discuss the analogy to 
relativistic space-time.