Construct a grammar that generates L = {a^p b^m c^n|n>=0, m>=0, p=m+n}

Question

Construct a grammar that generates L:

L = {a^p b^m c^n|n>=0, m>=0, p=m+n}

Till now I have attempted this much:

S->A
A->aAb|B
B->aBc|epsilon

Is my grammar right?

score 1 · Accepted Answer · answered Feb 15 '16 at 05:01

1

I can't give the mathematical proof, but let's try to enumerate the strings your grammar can produce:

ε, ac, aacc, aaaccc, ... (more same # of a and c), ab, aabb, aaabbb, ... (more same # of a and b), aacb, aaaccb, aaacbb, aaaaccbb, ... (more # a which is the same as # b + c)

Now does:

a^p b^m c^n

indicate that the order must be strictly fulfilled? i.e. a first then b then c. if yes, you can see yourself that b and c are actually swapped in your grammar.

answered Feb 15 '16 at 05:01

LeleDumbo

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Yes the order must be maintained( a followed by b and then c) How to fix the wrong swapping? – Rachit Belwariar Feb 15 '16 at 05:13
Ok, Now got it S->A A->aAc|B B->aBb|epsilon I guess this is the correct grammar. Thanks @LeleDumbo – Rachit Belwariar Feb 15 '16 at 05:25

Construct a grammar that generates L = {a^p b^m c^n|n>=0, m>=0, p=m+n}

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