A complexity measure for data flow models

For common data flow schemes, the number of copies of tokens made during a computation is demonstrated to be a Blum (1967) complexity measure. Results from abstract complexity theory then hold for the copy measure, suggesting, for example, that any implementation of a data flow processor will be limited by its ability to copy tokens. The copy measure is a natural measure of complexity for data flow calculations, and is distinct from the usual time or space measures. The result is generalized to a broader class of data flow schemas, including those with an apply operator. An example is also presented of a data flow scheme that makes no copies either by explicit copy nodes or by operators that release more than one token at a time. Calculation in this example proceeds by the repeated modification of a single token.