Slowdown invariance of timed regular expressions

Abstract

In critical systems, it is frequently essential to know whether the system satisfies a number of real-time constraints, usually specified in a real-time logic such as timed regular expressions. However, after having verified a system correct, changes in its environment may slow it down or speed it up, possibly invalidating the properties. Colombo et al. (1) have presented a theory of slowdown and speedup invariance to determine which specifications are safe with respect to system retiming, and applied the approach to duration calculus. In this paper we build upon their approach, applying it to timed regular expressions. We hence identify a fragment of the logic which is invariant under the speedup or slowdown of a system, enabling more resilient verification of properties written in the logic.