fs0: ? -> fs0, a -> fs1, b -> fs0.
fs1: ? -> fs0, a -> s2, b -> fs0, <a:b> -> fs3.
s2: ? -> fs0, a -> s2, b -> fs0, <a:b> -> fs3.
fs3: (no arcs)
Answer:
There is no unique answer. Any finite-state language or
relation can be described by an infinite number of equivalent regular
expressions. Some are simple, some more complicated. Perhaps the
simplest one in this case is
a -> b || a _ .#.
It denotes all pairs of strings that are identical except that any
final "a" that is preceded by another "a" in the upper-language string
gets replaced by "b" in the corresponding lower-language string. For
example, this transducer maps "baaa" into "baab". Another regular
expression describing the same relation is
[?* - [?* a a]] | [?* a a:b]
The diagram below represents the same network as the table above.
