Detecting Locally Distributed Predicates

In this article, we formalize locally distributed predicates, a concept previously introduced to address specific challenges associated with modular robotics and distributed debugging. A locally distributed predicate (LDP) is a novel construction for representing and detecting distributed properties in sparse-topology systems. Our previous work on LDPs presented empirical validation; here we show a formal model for two variants of the LDP algorithm, LDP-Basic and LDP-Snapshot, and establish performance bounds for these variants. We prove that LDP-Basic can detect strong stable predicates, that LDP-Snapshot can detect all stable predicates, and discuss their applicability to various distributed programming domains and to spatial computing in general. LDP detection in bounded-degree networks is shown to be scale-free, making the approach particularly attractive for specific topologies, even though LDPs are less efficient than snapshot algorithms in general distributed systems.