## Section: New Results

### Polychrony and Kahn Process Networks

Participants : Paul Le Guernic, Thierry Gautier.

We have started fundamental yet published research on reconsidering the polychronous model of computation with respect to Kahn Process Networks (KPN).

The first question is: are Signal programs KPNs? While synchronous operators are flow functions, polychronous operators (when, default) are not. But they are “synchronized” flow functions when we add a special value denoting meaningful absence to the domain of values. Then, a result is that a Signal specification denotes a flow function if it can be rewritten, using syntactic equivalence and clock calculus, as the composition of endochronous processes, such that the master clocks are free or input signals.

Considering now the question “are KPN Signal programs?”, we propose to extend Signal with an equation allowing to specify pure flow equality (in Signal+). Asynchronous composition can be defined as synchronous composition with flow equality (unbounded FIFOs). Then a synchronized program can be expressed as an unbounded FIFO program, composed with a set of constraints on bounds expressed as Signal equations.