Karine Altisen and Matthieu Moy

Causality Closure for a New Class of Curves in Real-Time Calculus - Full version (2011)

Causality Closure for a New Class of Curves in Real-Time Calculus - Full version (2011)

TR-2011-13.pdf

**Keywords:**Real-Time Calculus, Causality, Algorithms

**Abstract:**Real-Time Calculus (RTC) is a framework to analyze heterogeneous real-time systems that process event streams of data. The streams are characterized by arrival curves which 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. The property of causality on arrival curves essentially characterizes the absence of deadlock in the corresponding generator. A mathematical operation called causality closure transforms arbitrary curves into causal ones. In this paper, we extend the existing theory on causality to the class Upac of infinite curves represented by a finite set of points plus piecewise affine functions, where existing algorithms did not apply. We show how to apply the causality closure on this class of curves, prove that this causal representative is still in the class and give algorithms to compute it. This provides the tightest pair of curves among the curves which accept the same sets of streams.