Problem Detail: So I have a question: Give a CFG for ${a^i b^j : 2 i<j}$ And this is my approach: $Sto AB$ $Ato aAbmid varepsilon$ $Bto b mid bB$ A confirmation, or correction, along with how you tested(and tips for testing future of my problems) will be greatly appreciated thanks.
Asked By : Gaak
Answered By : Raphael
You can derive $aabbb$ which is not in the language, so your grammar is wrong. How did I find this? I observed that $A Rightarrow^* a^ib^i$ and $B Rightarrow^* b^j$ for all $i geq 0$, $j > 0$. It’s clear that this is wrong, and I looked for the smallest counter-example. You need to ensure that more than double as many $b$’s as $a$’s are generated.
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Question Source : http://cs.stackexchange.com/questions/11076
