Symbolic model checking for real-time systems
Information and Computation
Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environment
Journal of the ACM (JACM)
Formal Methods in System Design
Combining simulation and formal methods for system-level performance analysis
Proceedings of the conference on Design, automation and test in Europe: Proceedings
RTSS '07 Proceedings of the 28th IEEE International Real-Time Systems Symposium
An Algorithmic Toolbox for Network Calculus
Discrete Event Dynamic Systems
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
Causality closure for a new class of curves in real-time calculus
Proceedings of the 1st International Workshop on Worst-Case Traversal Time
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The Real-Time Calculus (RTC) [1] is a framework to analyze heterogeneous real-time systems that process event streams of data. The streams are characterized by pairs of curves, called arrival curves, that express upper and lower bounds on the number of events that may arrive over any specified time interval. System properties may then be computed using algebraic techniques in a compositional way. A wellknown limitation of RTC is that it cannot model systems with states and recent works [2,3,4,5] studied how to interface RTC curves with statebased models. Doing so, while trying, for example to generate a stream of events that satisfies some given pair of curves, we faced a causality problem [6]: it can be the case that, once having generated a finite prefix of an event stream, the generator deadlocks, since no extension of the prefix can satisfy the curves anymore. When trying to express the property of the curves with state-based models, one may face the same problem. This paper formally defines the problem on arrival curves, and gives algebraic ways to characterize causal pairs of curves, i.e. curves for which the problem cannot occur. Then, we provide algorithms to compute a causal pair of curves equivalent to a given curve, in several models. These algorithms provide a canonical representation for a pair of curves, which is the best pair of curves among the curves equivalent to the ones they take as input.