On the Relations Computable by a Classof Concurrent

We consider monotone input/output automata, which model a usefully large class of dataaow networks of indeterminate (or nonfunctional) processes. We obtain a characterization of the relations computable by these automata, which states that a relation R : X ! 2 Y (viewed as a \nondeterministic function") is the in-put/output relation of an automaton ii there exists a certain kind of Scott domain D, a continuous function F : X ! D ! Y ] and a continuous function G : X ! P(D), such that R(x) = F(x) y (G(x)) for all inputs x 2 X. Here P denotes a certain powerdomain operator, and y denotes the pointwise extension to the powerdomain of a function on the underlying domain. An attractive feature of this result is that it specializes to two subclasses of automata, determinate automata, for which G is single-valued, and semi-determinate au-tomata, for which G is a constant function. A corollary of the latter result is the impossibility of implementing \angelic merge" by a network of determinate processes and \innnity-fair merge" processes.