Finite Automata

Design context-free grammars for the following languages: the set of all strings with twice as many 0’s as 1’s.
JavaranchAsked:
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ozoCommented:
Is this homework?
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SuperdaveCommented:
Also it doesn't have anything to do with finite automata, which are "regular languages" and can't do that.
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GwynforWebCommented:
It is a well known grammar

S --> S1S0S0S | S0S1S0S | S0S0S1S | e

proving it does the job of course is a different matter.
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NeilHKCommented:
I can't claim this, I found it but take a look......

S --> S1S0S0 | S0S1S0 | S0S0S1 | e
  example
   generate this string      001001010100010
       S -->  S0S1S0
          --> S0S0S10S1S0
          --> 0010S1S0
          --> 0010S0S1S0S1S0
          --> 001001S0S1S00S1S0
          --> 00100101S0S1S000S1S0
          -->001001010100010
   Generate the string 111000000
        S --> S1S0S0
           --> S1S1S0S00S0
           --> S1S1S1S0S00S00S0
           --> 111000000
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GwynforWebCommented:
NeilHK,  You have copied and pasted my answer?
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NeilHKCommented:
GwynforWeb, Just an example of your answer Gwyn. As I said, I can not take credit for it.
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a0vanc01Commented:
S  -> S1 | S2 | S3
S1 -> 001S | 001 (lambda)
S2 -> 010S | 010(lambda)
S3 -> 100S | 100(lambda)
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ozoCommented:
GwynforWeb's answer is correct.
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