Symbolic simulation of dataflow synchronous programs with timers

The synchronous language Lustre and its descendants have long been used to program and model discrete con-trollers. Recent work shows how to mix discrete and continuous elements in a Lustre-like language called Zélus. The resulting hybrid programs are deterministic and can be simulated with a numerical solver. In this article, we focus on a subset of hybrid programs where continuous behaviors are expressed using timers, nondeterministic guards, and invariants, as in Timed Safety Automata. We propose a source-to-source compilation pass to generate discrete code that, coupled with standard operations on Difference-Bound Matrices, produces symbolic traces that each represent a set of concrete traces.