On the Suitability of Dissemination-centric Access Control Systems for Group-centric Sharing Full Proofs

1.1 g-SIS0 Model States States in g-SIS0 systems have the following fields. • S, the set of subjects • O, the set of objects • G, the set of groups • T , the set of times • >T , the total order on T • Time ∈ T , the current time • StrictJoin ⊆ S ×G× T , the record of strict join events • LiberalJoin ⊆ S ×G× T , the record of liberal join events • StrictLeave ⊆ S ×G× T , the record of strict leave events • LiberalLeave ⊆ S ×G× T , the record of liberal leave events • StrictAdd ⊆ O ×G× T , the record of strict add events • LiberalAdd ⊆ O ×G× T , the record of liberal add events • StrictRemove ⊆ O ×G× T , the record of strict remove events • LiberalRemove ⊆ O ×G× T , the record of liberal remove events