Section: New Results

Symbolic Simulation for a timed-automaton subset of Zélus

Participants : Guillaume Baudart, Timothy Bourke, Marc Pouzet.

Synchronous languages like Lustre are ideal for programming an important class of embedded controllers. Their discrete model of time and deterministic semantics facilitate the precise expression of reactive behaviors. That said, many systems are naturally modeled using physical timing constraints that almost inevitably involve some `timing nondeterminism' due to tolerances in requirements or uncertainties in implementations. Conversely, such constraints are readily modeled using Timed Automata, and simulated symbolically in Uppaal, but large-scale discrete-time behaviors are more cumbersome to express in such tools.

In this work, we combined existing techniques and data structures for Timed Safety Automata with typing and compilation techniques for synchronous languages to develop a novel programming language where discrete reactive logic can be mixed with nondeterministic continuous-time features. In particular, we developed an extension of Lustre and a specialization of Zélus for modeling real-time reactive systems, proposed a symbolic simulation scheme based on `sweeping', and showed how to implement it via source-to-source compilation. A type system, based on that of Zélus, ensures the correct composition of discrete-time and continuous-time elements.

Our proposal has been implemented using the Zélus compiler and a small library of operations on Difference-Bound Matrices (DBMs). Unlike the work around Uppaal, we do not address verification or treat industrial case studies. A future direction could be to verify programs in our `extended version of Lustre' by either generating C code and using the highly-tuned Uppaal DBM library, or combining symbolic techniques for Lustre programs with those for Timed Automata.

This work was presented at FDL 2017 [5]. A prototype implementation is available online.

This work is also described with extended examples in Baudart's PhD thesis [1] which was defended in March of 2017.