Interval Probabilistic Timed Graph Transformation Systems

Abstract

For complex distributed embedded probabilistic real-time systems, ensuring correctness of their software components is of great importance. The rule-based formalism of Probabilistic Timed Graph Transformation Systems (PTGTSs) allows for modeling and analysis of such systems where states can be represented by graphs and where timed and probabilistic behavior is important. In PTGTSs, probabilistic behavior is specified by assigning precise probabilities to rules. However, for embedded systems, only lower and upper probability bounds may be estimated because unknown physical effects may influence the probabilities possibly changing them over time.In this paper, we (a) introduce the formalism of Interval Probabilistic Timed Graph Transformation Systems (IPTGTSs) in which rules are equipped with probability intervals rather than precise probabilities and (b) extend the preexisting model checking approach for PTGTSs to IPTGTSs w.r.t. worst-case/best-case probabilistic timed reachability properties using an encoding of probability intervals. Moreover, we ensure that this adapted model checking approach is applicable to IPTGTSs for which the finiteness of the state space may only be a consequence of the timing constraints. Finally, in our evaluation, we apply an implementation of our model checking approach in AutoGraph to a running example.KeywordsCyber-physical systemsGraph transformation systemsInterval probabilistic timed systemsQualitative analysisQuantitative analysisModel checking