Doubt ?? confirmation

Question

Q. which is True/False??? plz confirm ???

a) L is regular <---------------->      Ê_a  DFA with single finite state .

b)                                                  Ê_a  Regular expression for L.

c)                                                   Ê_a   Regular expression with out * .

d) some CFL can accept by FA but every CFL not accepted by FA.

Answer 1

a) L is regular <---------------->      Ê_a  DFA with single finite state .   : False.There can be multiple final states.If it would have been for NFA then it is true because mutiple states can be ccombined into one by giving e-transitions.

b)                                                  Ê_a  Regular expression for L.True

c)                                                   Ê_a   Regular expression with out * .False:- Without * we will not be able to accept empty string,but DFA should accept empty string if it is in the language it is representing.We can use + to generate infinite language but e(epsillon) will not be generated by +.

d) some CFL can accept by FA but every CFL not accepted by FA.True,Every regular language is CFl also,so we can say regular will accept CFL if the language represented by CFL is regular.However it cant accept everything.e.g If L={a},its CFL also and regualr also and can be accepted by FA,but on other side if we take L={a^nb^n},it will not be accepted by FA

Comments

i think B is false because regular is all finite or some infinite lanugage .

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Regular may be finite or infinite.We can always make FA for regular grammer,and we can always write Regular expression from FA.So it must be true