Given an n-nodes network and an assertion G expressing its correctness, it is shown that G can be decomposed into collection of n local assertions and n.(n-1) “communication” assertions. The special case of a 2-nodes network is first examined, and it is shown how the notion of Galois connections in lattice theory is a basic tool for the assertion decomposition. The principles of a communication protocol that allow to maintain the resulting assertions are described. For the n-nodes network it is shown that assertion G induces Galois connections between any two parts of the network. General formulae for the local and communication assertions are found using this fact. It is also shown that the communication assertions do involve only a pair of nodes each one, which makes possible the use of techniques taken from the 2-nodes network for their maintenance. As an application example a distributed algorithm to solve the “2-out-of-3” problem is proposed.

In the literature on serializability (see [1]), a transaction is considered to be a finite sequence of operations. As a step towards the handling of more complex evolutions of processes, we assume in this paper that the sequence of operations performed by a transaction may be infinitely often repeated as for instance, might behave a pre-existing service process in an operating system. (Remark that the classical “critical section” problem can be viewed as a particular case of the serializability problem). Therefore, a behaviour of a system of transactions will be understood herein as an infinite behaviour.