A generalized transition graph (GTG) is composed of states, an alphabet of input letters, and directed edges between states labeled with regular expressions. An example GTG has three states - a start state, middle state, and final state. The edges are labeled with (ba + a)*, allowing strings to transition from the start to middle state or directly to the final state, and b* allowing transition from the middle to final state. This GTG accepts all strings without a double b.