Abstract: This invention provides a novel computer design that is capable of utilizing large numbers of very large scale integrated (VLSI) circuit chips as a basis for efficient high performance computation. This design is a static dataflow architecture of the type in which a plurality of dataflow processing elements communicate externally by means of input/output circuitry, and internally by means of packets sent through a routing network that implements a transmission path from any processing element to any other processing element. This design effects processing element transactions on data according to a distribution of instructions that is at most partially ordered. These instructions correspond to the nodes of a directed graph in which any pair of nodes connected by an arc corresponds to a predecessor-successor pair of instructions. Generally each predecessor instruction has one or more successor instructions, and each successor instruction has one or more predecessor instructions.