Changes

The task ahead is to chart a course from general ideas about ''transformational equivalence classes of graphs'' to a notion of ''differential analytic turing automata'' (DATA).  It may be a while before we get within sight of that goal, but it will provide a better measure of motivation to name the thread after the envisioned end rather than the more homely starting place.

The task ahead is to chart a course from general ideas about ''transformational equivalence classes of graphs'' to a notion of ''differential analytic turing automata'' (DATA).  It may be a while before we get within sight of that goal, but it will provide a better measure of motivation to name the thread after the envisioned end rather than the more homely starting place.

The basic idea is as follows.  One is given a set <math>\mathcal{G}</math> of graphs and a set <math>\mathcal{T}</math> of transformations rules <math>\operatorname{t} \in \mathcal{T},</math> each of which has the effect of taking graphs into graphs, <math>\operatorname{t} : \mathcal{G} \to \mathcal{G}.</math>  In the cases that we shall be studying, this set of transformation rules partitions the set of graphs into ''transformational equivalence classes'' (TECs).

The basic idea is as follows.  One is given a set <math>\mathcal{G}</math> of graphs and a set <math>\mathcal{T}</math> of transformation rules, where each rule <math>\operatorname{t} \in \mathcal{T}</math> has the effect of transforming graphs into graphs, <math>\operatorname{t} : \mathcal{G} \to \mathcal{G}.</math>  In the cases that we shall be studying, this set of transformation rules partitions the set of graphs into ''transformational equivalence classes'' (TECs).

There are many interesting excursions to be had here, but I will focus mainly on logical applications, and and so the TECs I talk about will almost always have the character of ''logical equivalence classes'' (LECs).

There are many interesting excursions to be had here, but I will focus mainly on logical applications, and and so the TECs I talk about will almost always have the character of ''logical equivalence classes'' (LECs).