Weaker forms of monotonicity for declarative networking: a more fine-grained answer to the calm-conjecture

The CALM-conjecture, first stated by Hellerstein [23] and proved in its revised form by Ameloot et al. [13] within the framework of relational transducer networks, asserts that a query has a coordination-free execution strategy if and only if the query is monotone. Zinn et al. [32] extended the framework of relational transducer networks to allow for specific data distribution strategies and showed that the nonmonotone win-move query is coordination-free for domain-guided data distributions. In this paper, we complete the story by equating increasingly larger classes of coordination-free computations with increasingly weaker forms of monotonicity and make Datalog variants explicit that capture each of these classes. One such fragment is based on stratified Datalog where rules are required to be connected with the exception of the last stratum. In addition, we characterize coordination-freeness as those computations that do not require knowledge about all other nodes in the network, and therefore, can not globally coordinate. The results in this paper can be interpreted as a more fine-grained answer to the CALM-conjecture.