The paper is concerned with global distributed processes having random communications graphs, in which individual processors may be randomly created or destroyed, and communications edges between individuals may change randomly, as in, for example, an insect colony. The paper investigates a general family of global processes that execute successfully in spite of occasional random changes in architecture during execution.

In his review, M. Day correctly points out that “it is important to model individuals realistically,” but then he incorrectly states, “this paper…assumes that each [individual] has essentially infinite storage.” This impression may have originated in a poorly stated assumption; on page 127 of the paper, the data types on which an individual must compute were “assume[d]…to be closed under finite subsets.” To avoid a requirement of infinite memory, it should have read, “under finite subsets of atoms from the local algebra.” Alternatively, this impression may have originated in several examples in which the size of individual memory is finite but system-dependent. Let n = | I | be the number of individuals; then in the seven examples given in the paper,

∏ ( i = 1 ,..., 7 )

Nevertheless, without making any assumptions on individual memory, we prove that monotonic processes (in Theorem 2) and five of the examples (in Theorem 4) can be expected to converge to an intended global state, in spite of random changes in system architecture. Theorem 2 and Theorem 4 were proved for systems having fixed finite local algebras for individual computing and requiring bounded individual memory; thus we have definitely not assumed “essentially infinite memory” for individuals. This paper defines and uses analytic methods and concepts--monotonicity, convergence, and continuity--in an investigation at the global level.