1.8 Exercises

1. In the lecture, we represented haha1 in Prolog as follows:

   initial(1).
final(4).
arc(1,2,h).
arc(2,3,a).
arc(3,4,!).
arc(3,2,h).

   But we could also have represented it like this:

   initial(1).
final(4).
arc(1,2,h).
arc(2,3,a).
arc(3,2,h).
arc(3,4,!).

   Does it make any difference which way we represent it?

2. Here's the code for recognize1 given in the lecture:

   recognize1(Node,[]) :-
    final(Node).
recognize1(Node_1,String) :-
    arc(Node_1,Node_2,Label),
    traverse1(Label,String,NewString),
    recognize1(Node_2,NewString).

   Suppose we changed it to this:

   recognize1(Node,[]) :-
    final(Node),!.
recognize1(Node_1,String) :-
    arc(Node_1,Node_2,Label),
    traverse1(Label,String,NewString),!,
    recognize1(Node_2,NewString).

   What effect would this change have? What sort of FSAs would not be affected by the change?

3. Write FSAs that generate the following languages:

   • where

   • where