# How i can use Mathematical induction to prove CFG production? [duplicate]

If I have production $$G_n$$

$$S \rightarrow A_i b_i \quad$$ for $$1 \le i \le n$$

$$A_i \rightarrow a_j A_i \mid a_j\quad$$ for $$1 \le i$$ and $$i \ne j$$

1. Prove $$G_n$$ is sub-productions from $$2n^2 - n$$
2. Prove $$G_n$$ is $$LR(0)$$ production from $$2^n + n^2 + n$$
• Welcome to MSe! It really help readability if you pose your questions using MathJax. I updated your question, but please verify I got it correct. Also, it helps the MSE Community know where you are having issues if you tell us what you have tried and where you are confused/stuck. Regards – Amzoti Jan 27 '13 at 17:16
• I understand what the productions of $G_n$ are, but what do you mean by ‘sub-productions from $2n^2-n$’ and ‘$LR(0)$ production from $2^n+n^2+n$’? $G_n$ has $n$ productions of the first type and $n^2-n$ of the second type, so it has $2n^2-n$ productions altogether; if that’s what the first question asks you to prove, it does not require induction. – Brian M. Scott Jan 27 '13 at 21:27
• First Request: i used math induction to prove, but i don't know if this way is true. Second: i don't know how prove – M.B Jan 28 '13 at 15:20
• I don't quite understand the phrasing of the question. Assuming it concerns a proof that the given grammar(s) generate(s) some language(s), I'm closing as a duplicate of the (new) reference question. – Raphael Apr 14 '13 at 19:11