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ID: 3551134 • Letter: #
Question
%3Cp%3E%3Cimg%20class%3D%22user-upload%22%20src%3D%0A%22http%3A%2F%2Fmedia.cheggcdn.com%2Fmedia%252F970%252F970d9a32-f860-494a-a070-7b7a5bfbc3a7%252FphpYZD1zo.png%22%0Aheight%3D%2295%22%20width%3D%22780%22%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EPlus%3C%2Fspan%3E%2C%3C%2Fp%3E%0A%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cimg%20class%3D%22user-upload%22%20src%3D%0A%22http%3A%2F%2Fmedia.cheggcdn.com%2Fmedia%252F382%252F382ea89b-5412-4609-a13a-b46bab07780d%252Fphpq4ZXVn.png%22%0Aheight%3D%2245%22%20width%3D%22551%22%20%2F%3E%3C%2Fp%3E%0AExplanation / Answer
L = {a^i b^j c^ k d^l }.
Language description: am bn consist of a followed by b where number of a are equal or more then number of b.
some example strings: {^, a, aa, aab, aabb, aaaab, ab......}
So there is always one a for one b but extra a are possible. infect string can be consist of a only. Also notice ^ null is a member of language because in ^ NumberOf(a) = NumberOf(b) = 0
How to write grammar for am bn?
In the grammar, there should be a rules such that if you add a b symbol you also add a a symbol.
anf this can be done with something like:
But this is incomplete because we need a rule to generate extra as for this rules are just below:
Combine two production rules into a single grammar CFG.
So you can generate any string consist of a also a and b in (am bn) pattern.
But in above grammar there is no way to generate ^ string.
So, Change this grammar like this:
this grammar can generate L = {a^i b^j c^ k d^l }.language.
Note: to generate ^ null string, I added an extra first step in grammar by adding S--> B | ^, So you can either add ^ or your string of symbol a and b. (now B plays role of S from previous grammar to generate equal numbers of a and b)
THE ABOVE GRAMMER IS AMBIGUOUS BECAUSE,
We were able to construct 2 distinct Derivations. Hence This Grammar is ambiguous.
"If a grammar produces at least 2 distinct parse tree or derivations, then the grammar is ambiguous."
I hope you get my answer. pls do rate :)
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