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{a^n b^m c^k | n > m + k}

My problem of understanding is how to create a new a before the b's if you create new c's.

Hopefully someone can help me out.

Peter Golfplatz
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    https://cs.stackexchange.com/q/18524/755 – D.W. May 27 '23 at 16:16
  • Please don't use images of text or math. This makes your question impossible to search and inaccessible to the visually impaired; we don't like that. Please transcribe text and mathematics. You can use LaTeX. Don't forget to give proper attribution to your sources! – D.W. Feb 22 '24 at 20:41

1 Answers1

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You can firstly spawn $k$ letter $c$'s providing an $a$ for every $c$ spawned, then start putting $m$ $b$'s between $a$ and $c$ adding $a$ for every $b$. Also letter $a$ can be created any number of times after all $b$ and $c$ letters are created. This approach can be done with the following CFG: $$G = (V, \Sigma, S, R), \: V = \{S, A, B, B', C, C'\} \cup \Sigma,$$ and the rules are $$R = \begin{cases} S \to AC, \\ S \to AB, \\ C \to ACC', \\ C \to AC', \\ C \to ABC', \\ B \to ABB', \\ B \to AB', \\ C' \to c, \\ C' \to e, \\ B' \to b, \\ B' \to e, \\ A \to Aa, \\ A \to a. \end{cases}$$ This grammar is definetely not the most beautiful and short, I have put some safety checks there. However, it demonstrates the idea of my solution.

aassegai
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