Constructive polychronous systems

Abstract. The synchronous paradigm provides a logical abstraction of time for reactive system design which allows automatic synthesis of embedded programs that behave in a predictable, timely and reactive manner. According to the synchrony hypothesis, a synchronous model reacts to input events and generates outputs that are immediately made available. But even though synchrony greatly simplifies design of complex systems, it often leads to rejecting models when data dependencies within a reaction are ill-specified, leading to causal cycles. Constructivity is a key property to guarantee that the output during each reaction can be algorithmically determined. Polychrony deviates from perfect synchrony by using a partially ordered or relational model of time. It captures the behaviors of (implicitly) multi-clocked data-flow networks and can analyze and synthesize them to GALS systems or to Kahn process net-works (KPNs). In this paper, we provide a unified constructive semantic framework, using structural operational semantics, which captures the behavior of both synchronous modules and multi-clocked polychronous processes. Along the way, we define the very first operational semantics of Signal.