Non Modularity and Expressibility for Nets of Relations

Data flow deeds with nets of concurrently communicating agents. But unlike other theories of concurrency, the main concern here is about the I(nput)-O(u-tput) behavior of a system. The Kahn principle states that for special dctermlnistic agents the Input-Output behavior of a net can bc obtained from the I-O behaviors of its components. The I-O behaviors of Kahn agents are sequential functions and the I-0 behavior of a net over such agents is obtained as the solution of an appropriate system of equations constructed from the functions computed by its components. One of important consequences of the Kahn principle and the properties of corresponding systems of equations is that nets over Kahn agents are I-O-su~sli~utive, i.e. if a subnet NI of a given net N is replaced by a net with the same 1-0 behavior then the I-O behavior of the overall net remains unchanged. In an attempt to generalize Kahn's results [3] to nondeterministic agents, Brock and Ackerman observed that for such nets subtitutivity fails. This fa~t was such a surprise when it was first observed in [2] that it is known as Brock Ackerman anomaly.