Verification of Contact Tracing Protocols via SMT-based Model Checking and Counting Abstraction

We present an automata-based model specifically devised to formalise abstractions of distributed protocols used by contact-tracing applications that combine Bluetooth and TCP/IP communication with a centralised server. The model provides pure names, store and read operations on both value and set variables, synchronous and asynchronous communication primitives for both kind of variables. A protocol configuration consists of the current state of a finite set of local states containing the states of individual devices. The transition system models the interaction between devices in the same physical location and between a single device and possible distributed servers. We will use the resulting model to specify the logic underlying contact tracing protocols. To automatically validate our formal models, we employ an extension of the Cubicle infinite-state model checker based on the Alt-Ergo SMT solver. To overcome spurious results due to the application of monotone abstraction, we propose to refine the predecessor computation adopted in Cubicle by combining predicates on the Theory of Arrays (as provided by Cubicle) with Presburger predicates inferred via a counting abstraction applied on a subset of control states of individual processes.