FOLA-demo80.html

Example #2

> ###############
### Problem 1
###############
InternalStates:={q0,q1,q2,q3}:
Alphabet:={a1,a2,a3}:
delta:=table():
delta[(q0,a1)]:=q0:
delta[(q0,a2)]:=q1:
delta[(q0,a3)]:=q2:
delta[(q1,a1)]:=q2:
delta[(q1,a2)]:=q3:
delta[(q1,a3)]:=q3:
delta[(q2,a1)]:=q2:
delta[(q2,a2)]:=q2:
delta[(q2,a3)]:=q2:
delta[(q3,a1)]:=q3:
delta[(q3,a2)]:=q1:
delta[(q3,a3)]:=q0:
InitialState := q0:
FinalStates:={q2,q3}:
dfa:=mkDFA(InternalStates,Alphabet,op(delta),InitialState,FinalStates);
partitionDFA(dfa);

(17.2.1)

> ################
### Problem 2
################
InternalStates:={q0,q1,q2,q3}:
Alphabet:={a1,a2,a3}:
delta:=table():
delta[(q0,a1)]:=q0:
delta[(q0,a2)]:=q2:
delta[(q0,a3)]:=q2:
delta[(q1,a1)]:=q3:
delta[(q1,a2)]:=q2:
delta[(q1,a3)]:=q0:
delta[(q2,a1)]:=q3:
delta[(q2,a2)]:=q3:
delta[(q2,a3)]:=q1:
delta[(q3,a1)]:=q1:
delta[(q3,a2)]:=q1:
delta[(q3,a3)]:=q2:
InitialState := q0:
FinalStates:={q1,q3}:
dfa:=mkDFA(InternalStates,Alphabet,op(delta),InitialState,FinalStates);
partitionDFA(dfa);

(17.2.2)

> #################
### Problem 3
#################
InternalStates:={q0,q1,q2,q3}:
Alphabet:={a1,a2,a3}:
delta:=table():
delta[(q0,a1)]:=q2:
delta[(q0,a2)]:=q0:
delta[(q0,a3)]:=q0:
delta[(q1,a1)]:=q0:
delta[(q1,a2)]:=q1:
delta[(q1,a3)]:=q3:
delta[(q2,a1)]:=q0:
delta[(q2,a2)]:=q1:
delta[(q2,a3)]:=q1:
delta[(q3,a1)]:=q0:
delta[(q3,a2)]:=q2:
delta[(q3,a3)]:=q1:
InitialState := q0:
FinalStates:={q0,q2}:
dfa:=mkDFA(InternalStates,Alphabet,op(delta),InitialState,FinalStates);
partitionDFA(dfa);

(17.2.3)

> #################
### Problem 4
#################
InternalStates:={q0,q1,q2,q3}:
Alphabet:={a1,a2,a3}:
delta:=delta:
delta[(q0,a1)]:=q1:
delta[(q0,a2)]:=q0:
delta[(q0,a3)]:=q3:
delta[(q1,a1)]:=q0:
delta[(q1,a2)]:=q3:
delta[(q1,a3)]:=q1:
delta[(q2,a1)]:=q1:
delta[(q2,a2)]:=q3:
delta[(q2,a3)]:=q0:
delta[(q3,a1)]:=q1:
delta[(q3,a2)]:=q2:
delta[(q3,a3)]:=q1:
InitialState := q0:
FinalStates:={q0,q3}:
dfa:=mkDFA(InternalStates,Alphabet,op(delta),InitialState,FinalStates);
partitionDFA(dfa);

(17.2.4)

> #################
### Problem 5
#################
InternalStates:={q0,q1,q2,q3}:
Alphabet:={a1,a2,a3}:
delta:=table():
delta[(q0,a1)]:=q3:
delta[(q0,a2)]:=q3:
delta[(q0,a3)]:=q3:
delta[(q1,a1)]:=q3:
delta[(q1,a2)]:=q1:
delta[(q1,a3)]:=q3:
delta[(q2,a1)]:=q2:
delta[(q2,a2)]:=q1:
delta[(q2,a3)]:=q1:
delta[(q3,a1)]:=q3:
delta[(q3,a2)]:=q1:
delta[(q3,a3)]:=q2:
InitialState := q0:
FinalStates:={q2,q3}:
dfa:=mkDFA(InternalStates,Alphabet,op(delta),InitialState,FinalStates);
partitionDFA(dfa);

(17.2.5)