Quantified Abstractions of Distributed Systems

When reasoning about distributed systems, it is essential to have information about the different kinds of nodes which compose the system, how many instances of each kind exist, and how nodes communicate with other nodes. In this paper we present a static-analysis-based approach which is able to provide information about the questions above. In order to cope with an unbounded number of nodes and an unbounded number of calls among them, the analysis performs an abstraction of the system producing a graph whose nodes may represent (infinitely) many concrete nodes and arcs represent any number of (infinitely) many calls among nodes. The crux of our approach is that the abstraction is enriched with upper bounds inferred by a resource analysis which limit the number of concrete instances which the nodes and arcs represent. The combined information provided by our approach has interesting applications such as debugging, optimizing and dimensioning distributed systems.