On the random structure of behavioural transition systems

Numerous properties of random graphs are highly predictable. Even by exploring a small part reliable observations are possible regarding their structure and size. An unfortunate observation is that standard models for random graphs, such as the Erdös–Rényi model, do not reflect the structure of the graphs that describe distributed systems and protocols. In this paper we propose to use the parallel composition of such random graphs to model ‘real’ state spaces. We show how we can use this structure to predict the size of state spaces, and we can use it to explain that software bugs are in practice far easier to find than predicted by the standard random graph models. By practical experiments we show that our new probabilistic model is an improvement over the standard model in predicting properties of transition systems representing realistic systems.