# NFA DFA RRG problem set Discussion

NFA DFA RRG problem set
Question 1: NFA union construction
Below are descriptions of two NFAs N1 and N2.
Convert them to an NFA recognizing L(N1) U L(N2).
N1:
states = {a,b,c,d}
input_alphabet = {0,1}
start_state = a
accept_states = {a}
delta =
a,1 -> b;
b,1 -> c;
b, -> a;
c,0 -> c;
c, -> b;
d,1 -> {b,c};
d, -> a;
N2:
states = {e,f,g,h}
input_alphabet = {0,1}
start_state = h
accept_states = {e,f,g}
delta =
e,0 -> {f,g};
e, -> {e,h};
f,0 -> g;
f, -> g;
g,1 -> {f,h};
g, -> e;
h,0 -> {g,h};
question2 : NFA concatentation construction
Below are descriptions of two NFAs N1 and N2.
Convert them to an NFA recognizing L(N1)L(N2).
N1:
states = {a,b,c,d}
input_alphabet = {0,1}
start_state = d
accept_states = {a,b}
delta =
a,0 -> d;
a, -> b;
b,0 -> c;
b, -> b;
c,0 -> {a,c};
c, -> a;
d,0 -> {b,d};
d,1 -> d;
N2:
states = {e,f,g,h}
input_alphabet = {0,1}
start_state = e
accept_states = {f,g,h}
delta =
e,0 -> {e,f};
f,1 -> {f,g};
g,1 -> h;
g, -> e;
h,1 -> f;
h, -> f;
question 3：NFA star construction
Below are descriptions of an NFA N.
Convert them to an NFA recognizing L(N)*.
N:
states = {a,b,c,d}
input_alphabet = {0,1}
start_state = d
accept_states = {b}
delta =
a,0 -> {a,d};
a,1 -> {b,d};
b,0 -> a;
c,0 -> c;
c, -> a;
d,0 -> d;
d,1 -> a;
d, -> a;
question 4: regex to NFA
Below is a description of a Regular Expression R.
Convert it to an NFA recognizing L(R).
R = ((1|01)|00)*
Question 5: NFA to DFA
Below is a description of an NFA N.
Convert it to a DFA recognizing L(N).
N:
states = {a,b,c}
input_alphabet = {0,1}
start_state = c
accept_states = {b,c}
delta =
a,0 -> a;
a, -> c;
b,1 -> c;
c,0 -> c;
c,1 -> b;
question 6: DFA to RRG
Below are descriptions of a DFA D.
Convert it to a right regular grammar (RRG) recognizing L(D) using the procedure described in lecture and in the textbook page 107). Submit your answer in a file with extension ‘.cfg’.
D:
states = {a,b,c,d,e,f,g,h}
input_alphabet = {0,1}
start_state = d
accept_states = {a,b,e,f,h}
delta =
a,0 -> f;
a,1 -> a;
b,0 -> h;
b,1 -> d;
c,0 -> c;
c,1 -> h;
d,0 -> h;
d,1 -> f;
e,0 -> c;
e,1 -> a;
f,0 -> g;
f,1 -> e;
g,0 -> d;
g,1 -> c;
h,0 -> b;
h,1 -> d;
question 7: DFA majority
Below are the descriptions of DFA D1, D2, and D3.
Convert them to a DFA that recognizes Maj(L(D1), L(D2), L(D3))
D1:
states = {a,b,c}
input_alphabet = {0,1}
start_state = c
accept_states = {b,c}
delta =
a,0 -> c;
a,1 -> c;
b,0 -> a;
b,1 -> c;
c,0 -> b;
c,1 -> a;
D2:
states = {d,e,f}
input_alphabet = {0,1}
start_state = e
accept_states = {d,e}
delta =
d,0 -> e;
d,1 -> e;
e,0 -> f;
e,1 -> f;
f,0 -> d;
f,1 -> d;
D3:
states = {g,h,i}
input_alphabet = {0,1}
start_state = h
accept_states = {h}
delta =
g,0 -> g;
g,1 -> h;
h,0 -> g;
h,1 -> g;
i,0 -> i;
i,1 -> i;
question 8: DFA to drop NFA
Below is the description of an NFA N.
Convert it to a NFA that recognizes Drop(L(N))
N:
states = {a,b,c,d}
input_alphabet = {0,1}
start_state = b
accept_states = {b}
delta =
a,1 -> {c,d};
a, -> a;
b,1 -> c;
c,0 -> b;
c, -> b;
d,1 -> b;
question 9: written

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