Pumping Lemma with length

I'm still need a bit of help with this. The example and assignment solutions aren't helping much as they are way too long and it's difficult to determine what is really required.

Does anyone have a few examples or maybe some advice on how to tackle these types of questions?

i also found too much waffle to keep my attention span so i summarised it, if you memorise this you can preety much use it for a PL question i reckon


- assume this lang is context free ..
...so there exists CFG with p live productions
...meaning we can apply PL with length
... meaning any word can be represented as uvxyz where length (vxy) =< 2^p
... and uvⁿxyⁿz is also in the language

-choose an appropriate word in the lang ( ok here you just replace any "n" you get in the questino with "2p) to try and pump eg if they give you aⁿbⁿc^2n-1 so say n=2p so

it becomes a^2pb^2pc^2p-1

then you start waffling :
- supose vxy consists entirely of a's, but then according to the PL the word uvvxyyz is also in the lanuage , this will have more than 2^p a's thoguh followed by b^2pc^2p-1.. and this isnt in the language

- repeat the above step using "entirely of b's , then again with c's to show how all those words cannot possibly be in the lanuage) at te end of it you concude that you cann't get it to work with the PL so it it not context free

Thank Iva!

thanks!!!

iva, you missed the cases where vxy can be a's and b's. Like, aaabbbb

sorry yes ,if the question is in the form aⁿbⁿ then you need that case of a mixture , when i was writing i was thinking of an example like aⁿbⁿcⁿ
GOOD LUCK EVERYONE FOR TOMRROW i'm outa here

just wrote, good luck guys (and gals, but we all know iva's gonna smash it )