Résumé
In this research report, we propose an enhancement of the compilation of synchronous programs with a combined numerical-Boolean abstraction. While our approach applies to synchronous dataflow languages in general, here, we consider the *signal* language for illustration. In the new abstraction, every signal in a program is associated with a pair of the form (clock, value), where clock is a Boolean function and value is a Boolean or numeric function. Given the performance level reached by recent progress in Satisfiability Modulo Theory (SMT), we use an SMT solver reason on this abstraction. Through sample examples, we show how our solution is used to determine absence of reaction captured by empty clocks; mutual exclusion captured by two or more clocks whose associated signals never occur at the same time; or hierarchical control of component activations via clock inclusion. We also show this analysis improves the quality of the code generated automatically by a compiler, e.g., a code with smaller footprint, or a code executed more efficiently thanks to optimizations enabled by the new abstraction. The implementation of the whole approach includes a translator of synchronous programs towards the standard input format of SMT solvers, and an *ad hoc* SMT solver that integrates advanced functionalities to cope with the issues of interest in this work.