/* File: dfa1.pl     System: SWI-Prolog  5.2.8
   Author: MM
   Date: 10/02/2003
   Title: Explore if the DFA defined is well defined.
   
   DFA accepts words that start with a.
   Alphabet={a,b}, States={0,1,2}   Favorable={1} start is state 0.
   Transition function is:
                delta(0,a)=1    delta(0,b)=2
                delta(1,a)=1    delta(1,b)=1
                delta(2,a)=2    delta(2,b)=2
   
   Load your file:
   ?- ['C://swimm/dfa21.pl'].
    Yes
   
   Is there a start state.
   ?- start(_).
    Yes
   
   Is there one or more favorable states?
   ?- favorable(_).
    Yes
   
   List the delta/3 describing the transition function?
   ?- listing(delta).
      
   Is there any trap state (for any words goes into itself)?
   ?- delta(S,a,S),delta(S,b,S).
    S = 1  % You type <ENTER>
    Yes
    
   Is there any trap state that is not favorable (final)?
   ?- delta(S,a,S),delta(S,b,S), not favorable(S).
    No
   
   Find the alphabet and put it in a list. Use findall/3
   Means: take all X with the property delta(_,X,_) and put them in list L.
   
   ?- findall(X,delta(_,X,_),L).
   
   Take the list and sort it.
   ?- findall(X,delta(_,X,_),L), sort(L,Res).
    
   Find the list of all favorable states.
   ?- findall(Q,favorable(Q),L).
   
   For a certain state print the list of all the states where you can go from it.
    ?- findall(X,delta(0,_,X),L),sort(L,Res).
      
    Check if from a state Q there are more than 2 arrows for the same letter
    (Check if our automaton is deterministic for a certain state)
    ?- findall(X,delta(0,a,X),L).
    L=
     
     I have to find if L has the length =1. Use predicate length/2. See example:
     ?- length([a,[b,c],d],Len).
      Len=3
   
     How many states are there?
      ?-  findall(X,delta(X,a,_),L),sort(L,R),length(R,N).
      
      After I found L let's see how big(long) it is.
     ?- findall(X,delta(0,a,X),L),length(L,Res).
      Res=1
     
     Let's check if it exaclty one arrow from letter a from state 0. 
     I cannot have two definitions for a from one state. 
     ?- findall(X,delta(0,a,X),L),length(L,Res),Res=1.
     
     Same idea, but easier.
      ?- findall(X,delta(0,a,X),L),length(L,1).
      
     Let's check if it exaclty two arrows point put of a certain state. 
     I cannot have two definitions for a from one state. 
      ?- findall(X,delta(0,_,X),L),length(L,2).
      
         
*************************************************/
/* This is the definition of your DFA in Prolog.
*/
    delta(0,a,1).
    delta(0,b,2).
    delta(1,a,1).
    delta(1,b,1).
    delta(2,a,2).
    delta(2,b,2).
    
    start(0).
    
    favorable(1).