# Model as Transition Graph

The figure 3.2 above shows a transition graph G, which is a possible visual representation of an corresponding finite automaton A. A possible formal description of the graph G is as follows:

with as a set of vertices, as a set of edges and as an input alphabet, which is used for the Symbols attached to the edges as labels. As alphabet we assume the small set . We can then write:

1. =
2. with =
3. =

Using the additional convention to mark all initial and all final vertices with a double line you can now read the graph representation as a description of the expected behavior. The automaton, which is here represented as a transition graph, starts in vertex 1. As long as the human person (the user) keys in B or C the edges are leading back to vertex 1. Only if the symbol is keyed in leads an edge to vertex 2. For a transition from vertex 2 to vertex 3 the user must key in the symbol , and then again to reach vertex 4, a final state. If the user makes a mistake during its way to the final vertex he will be set back to the initial vertex 1.

Gerd Doeben-Henisch 2010-03-03