Work-in-Progress: Partial-Order Reduction in Reachability-based Response-Time Analyses

The temporal correctness of safety-critical systems is typically guaranteed via a response-time analysis (RTA). However, as the systems become complex (e.g., parallel tasks running on a multicore platform), most existing RTAs either become pessimistic or do not scale with respect to e.g., the number of tasks or period values. To make a trade-off between accuracy and scalability, recently, a new reachability-based RTA called schedule-abstraction graph (SAG) has been introduced by Nasri et al. It explores the space of possible decisions that a scheduling policy can take while dispatching a set of tasks or jobs on processing resources. The analysis is at least three orders of magnitude faster than other exact RTAs and is able to identify many more schedulable task sets than the existing fixed-point iteration-based analyses. One fundamental limitation of the SAG analysis is that in its reachability graph, each edge can only account for a single scheduling decision. Therefore, the graph grows exponentially when there are large uncertainties in the release time or execution time of the jobs. In this paper, we improve the scalability of the SAG analysis by introducing partial-order reduction (POR) rules that allow combining multiple scheduling decisions on one edge and hence avoiding combinatorial exploration of all possible scheduling decisions. An empirical evaluation shows that our solution is able to reduce the runtime by five orders of magnitude and the number of explored states by 98%.