anonymous
  • anonymous
Let the alphabet = {a, b}. Part (a): Give a Context Free Grammar for the language {a^nb^m | n > 2m}. I have NO clue at all.
Computer Science
katieb
  • katieb
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anonymous
  • anonymous
if zero b's then there must be at least one a if one b then there must be at least three a's if two b's then tehre must be at least five a's and so on
anonymous
  • anonymous
also first should come a's and only then b's
anonymous
  • anonymous
so we start with S -> aQT (we must have at least one a) Q -> aQ | ε (we can generate any number of a's before b) T -> aaTb | ε (if we create at least one b we must put two a's before b)

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anonymous
  • anonymous
Wow! Thanks! Here is what I came up with this morning toying around. \[S_0 \rightarrow aaS_1b | aaS_1b | aS_1\] \[S_1 \rightarrow S_0\epsilon | a\] Is this equivalent?
anonymous
  • anonymous
no, for example you can't get just a, but according to rules you should be able to however maybe you made mistake by typing because if it will be S_1 -> S_0|ϵ|a i think it would be ok and aaS_1b is same as aaS_1b so why you mention it 2 times? :D
anonymous
  • anonymous
Yes you are right, I mistyped, and my computer was acting up. I did have S1->S0 | epsilon | a. Thanks for the help!

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