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Certain basic problems in integration and extreme miniaturization of electronic systems may require new forms of device structure. A device structure that shows promise is hypothesized in this paper. The device is not discrete; it is rather a distributed "line," with active and passive processes so distributed that a signal propagates along the line without attenuation, much as a burning zone moves along a fuse or an ionic discharge along a nerve axon. It is shown that lines of this type can be interconnected in certain direct ways so that complete logic capability can be achieved with networks of such lines alone. Techniques of logical synthesis of these networks are introduced. Certain special properties of systems built in this fashion are delineated, especially properties that appear to be significant for the synthesis of highly-miniaturized systems. There is some discussion of physical realizability of distributed electronic structures.