Relating computation and time

In this paper, we examine the relation between the actions of a computation and the nature of time associated with the execution. Using a method suggested by Whitrow, we first define an instant of time in terms of computational actions and then show that the set of such instants is isomorphic with the reals provided it satisfies certain well-known properties. Some of these properties can be derived from a straightforward definition of actions and their ordering, but we also provide necessary and sufficient conditions for proving the denseness of the set. We then show how different assumptions about computations relate to the requirements for denseness. From this, it can be seen that the apparent choice between representing computational time by a discrete domain, an arbitrary dense domain and the real domain, for example, is really a choice between different computational models