Context-Free Grammar (CFG) Example: {a^i b^j c^k : i at most j+k}

Here we create a context-free grammar (CFG) for the language {a^i b^j c^k : i is at most j+k}. This is not inherently a hard language, since we take advantage of the fact that i (the number of a's at the front) is at most j+k (the sum of numbers of b's and c's). Therefore, we can match at most one "a" with every "b", and same with the "c"s. We have to use a different variable (at least in this CFG) to process the b's since there is an order on where the b's appear in the string (they're in the middle).

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I am a professor of Computer Science, and am passionate about it. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.

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[shiewhun]

Hello,
Can you please tell me where to start when trying to get the gist of CFGs?
Or can you say something about why they exist? What problems do they exist to solve in Computer Science?

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Gonzalez Kimberly Gonzalez Jason Gonzalez Anthony

[hussainshaikh]

Sir can u tell from which book u have taken