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If L is a language defined by : L = { awa | w ∈ {a, b}* },

is aa a string of the language L? (notice that w is being null string here)

batman
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2 Answers2

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According to you definition it seems L consists only of two words aba and aaa.

EDIT: after you have edited the question I can say yes "aa" is a word of this language w ∈ {a, b}* means zero or more chars of this alphabet and thus w may have zero chars and be empty.

Ivaylo Strandjev
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  • can't `w` be any combination of a's and b's ? something like : `abababa` ? – batman Jan 22 '13 at 14:54
  • At least the notation I have seen would declare such language as: `L = { awa | w ∈ {a, b}* } ` Note the star to indicate zero or more of. – Ivaylo Strandjev Jan 22 '13 at 14:57
  • Then yes `aa` is a word of the language – Ivaylo Strandjev Jan 22 '13 at 14:58
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    @abierto I am sorry but what you say definitely is not true. You may see I have posted a comment that made the OP change the question, my answer was correct before the edit and my explanation of the comment **before** the OP change the question is again the only thing I used in my answer. I can guarantee I have not used any information in your answer in any way. Of course you are free to believe me or not – Ivaylo Strandjev Jan 22 '13 at 15:07
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Your Problem can be restated as this. 

L= a(a|b)*a

Which translates into intuition as "Strings that begin with and end with 'a'". So naturally, 'aa' is a valid string.

I hope this answers your question.

damith219
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