In the NOT-PUMPING PROPERTY, shouldn't it be like "u v^i x y^i z doesn't belong to L for SOME i>=0" ( in the video we see "for ALL i>=0" ). When we use the pumping lemma, we always try to find just a single counterexample of i for which u v^i x y^i z doesn't belong to L. As we see the case of both pumping up and pumping down in some examples, sometimes "pumping up" preserves the pumping property, but "pumping down" doesn't.
Attention! In case 1 itself your vxy exceeds your pumping length. Can we contradict the basic condition to prove something by contradiction? lol I mean could we completely ignore the conditions |vy|>0 and |vxy|
He mentions at the end of the example that the other conditions may be violated as well, and could be used to show that the division of the word where v and y include "a"s and "c"s respectively, but there's no need too use that condition as even without using it we've shown the language is not context free
@hhp3, Does case 1 showed in 30.:00 have some problems? because if left out all "b"s as x, then your |vxy| will greater than p, that doesn't satisfy pumping lemma. Am I right, plz?
Yes, but you may find an i that actually belongs in the language. For example, choosing i = 1 in his example would have resulted in a string that belongs in the language. If this occurs, just pick another i and once you found an i that causes the string to not belong in the language, then you proved the language is not context-free by contradiction. :)
P is alphabet dependent. To know what p is you'd have to know both the rules set and the alphabet set. Every finite subset of a language (finite subset of strings in a given alphabet) can be trivially represented by regular expressions (just expand the alphabet). This alphabet can be reduced then, by applying some CFG. Going further, one can make some practical deductions about the nature of processes at hand by estimation of both storage space and computational power of the device.
These lectures are great but they'd be 30x better if you were to watch the video after you record it and rewrite your train of thought when teaching them and record it again more fluidly. You jump around a lot and you can tell that you forget where you were going and then start explaining something else and that's where I lose you. Just put a bit more effort into how you fluidly explain the train of thought needed to understand this concepts and to go through these problems. It would also make these videos sooo much shorter than they are.
Ryan Sloop, please forward me a link to an original multi-hour video series on a graduate-level scientific theory topic that YOU HAVE PRODUCED, so I can see how it should be done right. Until then, remember rule #1: "Don't complain, criticize, or condemn."
I think this video is very clear and understandable. My teachers at the the university I attend, could explain pumping lemmas in a very confusing way. The jumping to the logic part was good. DR hhp3 gives reminders of other topics, that are necessary to understand the actual topic. I really like this, because the other teachers at the university usually omit prerequisites and conveniently respond with "you should already know that". hhp3 lectures with giving all the necessary other topics like how to prove something indirectly. Only complaint could be image quality but so far it is readable so it's okay. It is quality content.
@@hhp3 This is not a rule of scientific discourse but one of political correctness... This is not how the science was built. In fact, it can be traced to some dark periods in the history of science. (and some rules of scientifically based dydactics seem to be emerging)
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These lectures are very helpful and easy to understand. Please upgrade the video quality!
Perhaps the best explanation of pumping lemma.. Thanks a lot.
In the NOT-PUMPING PROPERTY, shouldn't it be like "u v^i x y^i z doesn't belong to L for SOME i>=0" ( in the video we see "for ALL i>=0" ). When we use the pumping lemma, we always try to find just a single counterexample of i for which u v^i x y^i z doesn't belong to L. As we see the case of both pumping up and pumping down in some examples, sometimes "pumping up" preserves the pumping property, but "pumping down" doesn't.
Yes , you are correct.
Low quality footage, high quality teacher!
Attention!
In case 1 itself your vxy exceeds your pumping length. Can we contradict the basic condition to prove something by contradiction? lol I mean could we completely ignore the conditions |vy|>0 and |vxy|
Excellent explanation, really wish you are my professor
the best tutorial out there. Thank you
I really like this explanation of building a proof by contradiction.
Very good explanation. But I just wonder, why sometimes you used "pumping up" and sometimes "pumping down"?
Awesome video, but the quality of resolution is really bad :( Anyway, thank you for a very well made learning material.
at 31:11 seems theres a problem in the example
you chose vxy that their length is bigger than p
THIS
Exactly. Why is nobody asking? Are we the only dumb guys here?
He mentions at the end of the example that the other conditions may be violated as well, and could be used to show that the division of the word where v and y include "a"s and "c"s respectively, but there's no need too use that condition as even without using it we've shown the language is not context free
@hhp3, Does case 1 showed in 30.:00 have some problems? because if left out all "b"s as x, then your |vxy| will greater than p, that doesn't satisfy pumping lemma. Am I right, plz?
Is there a reason why you chose to pump down instead of up and vice versa at times? It would have worked either way right?
Yes, but you may find an i that actually belongs in the language. For example, choosing i = 1 in his example would have resulted in a string that belongs in the language. If this occurs, just pick another i and once you found an i that causes the string to not belong in the language, then you proved the language is not context-free by contradiction. :)
your videos are amazing ... I wish video quality was better ...
Great videos, thanks for uploading
Very nice but there's one thing I'm unclear about. DO WE KNOW WHAT P IS???
P is alphabet dependent. To know what p is you'd have to know both the rules set and the alphabet set. Every finite subset of a language (finite subset of strings in a given alphabet) can be trivially represented by regular expressions (just expand the alphabet). This alphabet can be reduced then, by applying some CFG. Going further, one can make some practical deductions about the nature of processes at hand by estimation of both storage space and computational power of the device.
Great explanation. Thank you.
Amazing video, super clear. The quality pretty bad though
Thanks!
Thank you ~
These lectures are great but they'd be 30x better if you were to watch the video after you record it and rewrite your train of thought when teaching them and record it again more fluidly. You jump around a lot and you can tell that you forget where you were going and then start explaining something else and that's where I lose you. Just put a bit more effort into how you fluidly explain the train of thought needed to understand this concepts and to go through these problems. It would also make these videos sooo much shorter than they are.
Ryan Sloop, please forward me a link to an original multi-hour video series on a graduate-level scientific theory topic that YOU HAVE PRODUCED, so I can see how it should be done right. Until then, remember rule #1: "Don't complain, criticize, or condemn."
I think this video is very clear and understandable. My teachers at the the university I attend, could explain pumping lemmas in a very confusing way. The jumping to the logic part was good. DR hhp3 gives reminders of other topics, that are necessary to understand the actual topic. I really like this, because the other teachers at the university usually omit prerequisites and conveniently respond with "you should already know that". hhp3 lectures with giving all the necessary other topics like how to prove something indirectly. Only complaint could be image quality but so far it is readable so it's okay. It is quality content.
@@hhp3 This is not a rule of scientific discourse but one of political correctness... This is not how the science was built. In fact, it can be traced to some dark periods in the history of science. (and some rules of scientifically based dydactics seem to be emerging)
@@hhp3 Very funny. Way to put Ryan Sloop in his place.
Horrible camera. Such a shame. I really like the coursework. But the video is a pain.
There is a copy of your vid with 11k views! Report it!
I'm really learning from these, but I think you mislabeled this video.
Terrible explanation.
how come?
Are you serious?
I think he was expecting a Movie Trailer for the Pumping Lemma for Context Free Languages *badum tsss*