Network algebra for synchronous and asynchronous dataflow

Abstract

Network algebra (NA) is proposed as a uniform algebraic framework for the description (and analysis) of dataflow networks. The core of this algebraic setting is provided by an equational theory called Basic Network Algebra (BNA). It constitutes a selection of primitives and identities from the algebra of flownomials due to (Ste86) and (CaS88&89). Both synchronous and asynchronous dataflow networks are then investigated from the viewpoint of network algebra. To this end the NA primitives are de ned such that the identities of BNA hold. These axioms are particularly strict about the role of the connections, which will be called flows of data. We describe three interpretations of the connections that satisfy the BNA identities: minimal stream delayers, stream delayers and stream retimers. Each of the above possibilities leads to a class of dataflow networks, synchronous dataflow networks, asynchronous dataflow networks and fully asynchronous dataflow networks, respectively. For each case stream transformer and process algebra models are introduced and compared.