On the Expressive Power of Indeterminate Network Primitives

Abstract

It is well known that a fair merge primitive leads to unbounded indeterminacy. In this paper we show that unbounded indeterminacy cannot express a fair merge in the setting of Kahn-style dataflow networks. Intuitively, unbounded indeterminacy can be used to program a fair merge when it is guaranteed that data will always be available. But such schemes rely on predictive scheduling and they may fail if one of the inputs to the merge is a finite stream. It is reasonable to expect that if one were to add a primitive which "knows how to avoid bottom" (so called "angelic merge") then one could use this in conjunction with unbounded choice in order to produce a fair merge. Somewhat surprisingly, this expectation is incorrect as we show in this paper. The method we use to prove this is to identify a property which generalises monotonicity to indeterminate networks and then show that this property is possessed by determinate networks and by unbounded choice and by angelic merge but not by fair merge. It appears that there is a hierarchy of inequivalent indeterminate primitives all of which feature some form of unbounded indeterminacy.