A Simple and Flexible Timing Constraint Logic

Formats for describing timing behaviors range from fixed menus of standard patterns, to fully open-ended behavioral definitions; of which some may be supported by formal semantic underpinnings, while others are better characterized as primarily informal notations. Timing descriptions that allow flexible extension within a fully formalized framework constitute a particularly interesting area in this respect. We present a small logic for expressing timing constraints in such an open-ended fashion, sprung out of our work with timing constraint semantics in the TIMMO-2-USE project [15]. The result is a non-modal, first-order logic over reals and sets of reals, which references the constrained objects solely in terms of event occurrences. Both finite and infinite behaviors may be expressed, and a core feature of the logic is the ability to restrict any constraint to just the finite ranges when a certain system mode is active. Full syntactic and semantic definitions of our formula language are given, and as an indicator of its expressiveness, we show how to express all constraint forms currently defined by TIMMO-2-USE and AUTOSAR. A separate section deals with the support for mode-dependencies that have been proposed for both frameworks, and we demonstrate by an example how our generic mode-restriction mechanism formalizes the details of such an extension.