The polychronous model of computation and Kahn process networks

In 1974, Gilles Khan defined a seminal semantic model for asynchronous dataflow programming that would then be called as the eponymous Kahn process networks (KPN) and instantiated in as many models of the so-called DPN hierarchy as domain-specific fields of information processing from digital signal processing to hybrid cyber-physical systems. Among these, synchronous programming models have had an important impact in the specific domain of embedded software design. In this paper, we consider an instance of what seems to be one of the many synchronous models of computation: polychrony, initiated by the dataflow language Signal and its multi-clock (i.e. polychronous) model of computation and, later on, CCSL (clock constraints specification language). We provide an in-depth study of its semantic relationship with respect to the original definition of KPNs and hint toward the idea of polychrony as a methodology to locally synchronize (abstractions of) globally asynchronous processes. In particular, we formally define the property, referred to as “polyendochrony”, that allows one to consider a given desynchronized network of synchronous Signal processes (a GALS architecture) as the implementation of a corresponding KPN model (an asynchronous network of Khan-deterministic functions). For this class of networks, we formalize the Signal program analysis and transformations that define synchronous clusters of Signal processes of guaranteed deterministic behavior in an asynchronous network, that is, without synchronizing communications in the entire network. This definition yields a new strategy of multi-threaded code generation that is available in the open-source Polychrony toolset of the Signal language and blurs the limits between the asynchronous and polychronous models of computation.