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Dijkstra E W. A note on two problems in connexion with graphs. We consider a graph with n vertices, all pairs of which are connected by an edge; each edge is of given positive length. The following two basic problems are solved. Problem 1: construct the tree of minimal total length between the n vertices. (A tree is a graph with one and only one path… (More)

So-called “guarded commands” are introduced as a building block for alternative and repetitive constructs that allow nondeterministic program components for which at least the activity evoked, but possibly even the final state, is not necessarily uniquely determined by the initial state. For the formal derivation of programs expressed in terms… (More)

As an example of cooperation between sequential processes with very little mutual interference despite frequent manipulations of a large shared data space, a technique is developed which allows nearly all of the activity needed for garbage detection and collection to be performed by an additional processor operating concurrently with the processor devoted… (More)

The purpose of this paper is twofold, viz. to present a new [0] algorithm for the detection of the termination of a distributed computation and to demonstrate how the algorithm can be derived in a number of steps. We consider N machines, each of which is either active or passive. Only active machines send so-called 'messages' to other machines; message… (More)