A theorem on the characteristics of non-sequential processes

Abstract

Real non-sequential processes can be described in a consistent way if they are assumed to satisfy a certain density property. Density as defined in [1] can be interpreted as postulating that a “global state” consists of a “progress snap-shot” of all single activities which constitute it.

The present report shows that postulating density amounts to postulating that (a) each single history of a process is either infinite or has a first cause (but not both), and (b) each single future of a process is either infinite or has a last effect (but not both). This result is interpreted and applied to the question of Turing-computability.