Constructing CFG from instructions where you have an OR

Asked May 14 '17 at 16:47

Active May 14 '17 at 17:58

Viewed 23 times

My question is: What tips or ideas do you have when you're gonna construct a CFG out of these instructions? If we only had 0 < i <= k, it'd be more straight forward if you ask me, but when we have an OR there, how should I approach it?

edit:

I just realized I could rewrite the language and then define the CFG as S -> L1 | L2 whereas L1 and L2 is the union shown in the image

However, I still am not very sure if this would be the easiest way. Therefore, I'd still be happy if someone could show me an example of how to construct this CFG.

edited May 14 '17 at 17:58

Raphael

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asked May 14 '17 at 16:47

Dan Danielson

After looking around, I found similar threads and tips. – Dan Danielson May 14 '17 at 16:57
(You should use LaTeX instead of images.) – chi May 14 '17 at 17:08
Oh, I noticed you were using mathjax or something but I had already made latex with an editor already. – Dan Danielson May 14 '17 at 17:12
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Your solution is perfect and simple, as long as the constituent languages are indeed context-free. – Yuval Filmus May 14 '17 at 17:21
I will make an attempt at it, and then come back with what I got as a result. – Dan Danielson May 14 '17 at 17:22
Hint: sometimes it helps rewriting ${f(n,m) | n,m\in\mathbb{N}, n\leq m }$ as ${f(n,n+k) | n,k\in\mathbb{N} }$ – chi May 14 '17 at 19:11

Constructing CFG from instructions where you have an OR

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