The Boolean Logic of Set Sharing Analysis

We show that Jacobs and Langen's domain for set-sharing analysis is isomorphic to the domain of positive Boolean functions, introduced by Marriott and Søndergaard for groundness dependency analysis. Viewing a set-sharing description as a minterm representation of a Boolean function leads to re-casting sharing analysis as an instantiation dependency analysis. The key idea is to view the sets of variables in a sharing domain element as the models of a Boolean function. In this way, sharing sets are precisely dual negated positive Boolean functions. This new view improves our understanding of sharing analysis considerably and opens up new avenues for the efficient implementation of this kind of analysis, for example using ROBDDs. To this end we express Jacobs and Langen's abstract operations for set sharing in logical form