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Given a language L, define Li as follows:
L0 = {ε}
Li = Li-1∙L for all i>0
The order of a language L is defined as the smallest k such that Lk=Lk+1. Consider the language L1 (over alphabet 0) accepted by the following automaton.

The order of L1 is ______ . Note -This was Numerical Type question.
  • a)
    2
  • b)
    3
  • c)
    1
  • d)
    None
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Given a language L, define Lias follows:L0= {ε}Li= Li-1∙...
L1 = ε + 0(00)* L0 = ε L1 = ε . (ε + 0(00)*)     = ε + 0(00)* = L1 L2 = L1 . L1 = L1 . L1     = (ε + 0(00)*) (ε + 0(00)*)     = ε + 0(00)* + 0(00)* + 0(00)* . 0(00)*     = ε + 0(00)* + 0(00)* 0(00)* = 0* Given automaton contains epsilon and even number of 0's and odd numbers of 0's. L3 = L2 . L1     = {0*} . {ε + 0(00)*} = 0* 0(00)* = 0* So, L2 = L3 = L2+1 So, smallest value of k = 2
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Given a language L, define Lias follows:L0= {ε}Li= Li-1∙L for all i>0The order of a language L is defined as the smallest k such that Lk=Lk+1. Consider the language L1(over alphabet 0) accepted by the following automaton.The order of L1is ______ .Note -This was Numerical Type question.a)2b)3c)1d)NoneCorrect answer is option 'A'. Can you explain this answer?
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