Timed Input/Output Determinacy for Tasks with Precedence Constraints

We define a timing language that supports the design and implementation of embedded control software. The language is inspired by the Logical Execution Time (LET) paradigm of Giotto, but combines it with classical precedence constraints on tasks. A program specifies multiple modes of operation, where each mode consists of a set of periodically activated sensors, actuators, tasks, and mode switches. Unlike in Giotto, sensors, actuators, and tasks may have non-zero offsets, and tasks may have deadlines smaller than periods. Tasks may read from sensors and other tasks and write to actuators and other tasks, thus inducing a precedence relation on the tasks of each mode. Communication between tasks with different periods may only occur at user-defined time instants in order to avoid race conditions and priority inversion. Given task WCETs, we schedule programs in two phases: (1) a polynomial global check of WCET-independent constraints on mode switching, and (2) a polynomial local check of WCET-dependent schedulability of each mode independently of mode switching. We show that scheduling modes separately according to EDF with precedence constraints is a sufficient (and, provided that all modes are reachable, necessary) criterion for global program schedulability. We also present a compiler with full support for the above constructs and discuss a case study of a control problem written in our language.