Analysis of Periodic Clock Relations in Polychronous Systems

The polychronous (synchronous, multiclocked) language Signal is used for the design and analysis of reactive systems. For the purpose of modeling eventdriven systems, we consider an extension of the polychronousmodel of computation of Signal with periodic equations denoted by ultimately periodic infinite words. These equations express periodic constraints on the signals of programs, that can be used to enrich the existing clock calculus of Signal. Thanks to this more powerful clock calculus, the communications between processes using periodic equations can be analysed to guarantee their correctness. In particular, the maximal size of buffers is formally evaluated. We illustrate the design of so-defined periodic systems using a 4-stroke engine example.