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Question

Write the Regular expression using arden’s lemma

Answer 1

A→ epsilon      (1)
B→ Aa + Da     (2)
C→ Bb             (3)
D→ Ab + Bb      (4)

Sub (1) in (2) and (1) in (4)

B→ a + Da  (5)

D→ b + Bb  (6)

Sub (6) in (5)

B→ a + (b + Bb)a

B→ a + ba + Bba

B→ (a+ba)(ba)*    (7)[On applying lemma]

Sub (7) in (3)

C→ (a+ba)(ba)*b

Regular Expression is the sum of final states

RE = A + C = epsilon + (a+ba)(ba)*b

Answer 2

From the above diagram, Starting state is A which takes epsilon as the value, since it is the final state as well either it will end here or it will take another value a which leads to state B or b which leads to state C I.e A- epsilon B- A(a) + D(a) C- B(b) D- A(a) + B(b) The string will continue as a+ba)(ba)* from state B and end at C by taking b as final value Final answer is.. ^+(a+ba)(ba)*b