On the random structure of behavioural transition systems

Random graphs have the property that they are very 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 we find in behavioural modelling. In this paper we propose an alternative model, which we show to be a better reflection of ‘real’ state spaces. We show how we can use this structure to predict the size of state spaces, and we show that in this model software bugs are much easier to find than in the more standard random graph models. Not only gives this theoretical evidence that testing might be more effective than thought by some, but it also gives means to quantify the amount of residual errors based on a limited number of test runs.