Time distance-based computation of the DBM over-approximation of preemptive real-time systems

Abstract

The verification of preemptive real-time systems is a crucial aspect in ensuring their correctness and reliability to meet strict time constraints. Generally, the analysis of the behaviors of such systems requires the computation of the reachability graphs encoding their state space. However, the construction of the latter is computationally expensive and resource-consuming as it involves, for each graph node, managing and solving polyhedral constraints whose complexity is exponential.In this paper, we explore a novel approach that builds an over-approximation of the state space of preemptive real-time systems. Our graph construction extends the expression of a node to the time-distance system that encodes the quantitative properties of past-fired subsequences. This makes it possible to restore relevant time information that is used to compute in a polynomial time a tighter difference bound matrix over-approximation of the polyhedral constraints. We show that the obtained graph is more appropriate to restore the quantitative properties of the model. The simulation results show that our graphs are almost of the same size as the exact graphs, while improving by far the times needed for their computation.