Towards a Basis for Endochronous Functions in Dataflow Process Networks

To ensure deterministic computations, nodes of Kahn process networks must implement sequential functions with blocking read methods. However, while the Kahn criteria are sufficient to ensure determinism, they are not necessary to ensure determinism. While it is difficult to define precise properties of nodes to ensure determinism of dataflow process networks, there are known classes of functions, such as endochronous and stable functions, that are more general than sequential functions and still ensure determinism. Endochronous functions are also of practical interest for desynchronizing systems, which is possible when a synchronous system does not react to the absence of values, so it does not need its clock and is instead triggered only by the arrival of data values. Basic nodes for defining the set of sequential functions are known. However, since the set of endochronous functions is larger than the set of sequential functions, the question arises which additional basic nodes are needed in dataflow process networks to define the endochronous functions.This paper discusses conditions that must hold for such a set of basic endochronous nodes, and presents examples of endochronous functions that must be represented in any case. In particular, we thereby focus on boolean endochronous functions so that we can reason about a finite set of functions that can be characterized by disjoint prime implicants.CCS CONCEPTS• Computer systems organization $\rightarrow$ Data flow architectures; • Software and its engineering $\rightarrow$ Data flow architectures; Synchronization; • Theory of computation $\rightarrow$ Rewrite systems; Pattern matching; Operational semantics.