# Recent questions tagged pumping-lemma

@Praveen Saini @Lakshman Patel RJIT @Digvijay Pandey Just wanted to ask doubt, If the minimum pumping length of the language can be 0 for any language? I think it should not be as any string will either be accepted or rejected.
1 vote
The language is : number of zeroes=number of ones(which can be done by a deterministic Push down automata) say w=11101000 now we divide it to 5 parts u,v,w,x,y , where u=1 v=110 w=1 x=00 y=0 L=u.(v*i).w.(x*i).y such that i>=0 but when we put i=0 the ... . This shows that the language is not in L . But as the language can be done by a PDA , it should not have failed ,or do i not understand it ?
How can I explain that this language- L= { a<sup>n</sup> b<sup>l</sup> : n ≠ l } is not regular. [USE PUMPING LEMMA OR CLOSURE PROPERTIES] This question is under a book named An introduction to formal languages and automata' but the explanation isn't ... it to me in an understandable manner and show how you exactly arrived at the solution? That would be a great help to me. Thanks in advance
How to prove L={a ^n^2:n≥0} is not context free using Pumping Lemma?
Is it necessary for the CFL string lenghts to be in AP if the alphabet is a singleton set?
1 vote
Show that the language $L = \{w \epsilon \{a, b, c\}^*: n_a(w) + n_b(w) = n_c(w)\}$ is context-free but not linear. I understand that a PDA can be constructed for this, but what I don't get is: can't we use the pumping lemma to show that the strings ... think they can all be handled this way such that $w_i$ won't be in $L$. But this language is context-free, so where am I going wrong with this?
For $\Sigma = \{a ,b \}$, let us consider the regular language $L=\{x \mid x = a^{2+3k} \text{ or } x=b^{10+12k}, k \geq 0\}$. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$ ? $3$ $5$ $9$ $24$
A language $L$ satisfies the Pumping Lemma for regular languages, and also the Pumping Lemma for context-free languages. Which of the following statements about $L$ is TRUE? $L$ is necessarily a regular language. $L$ is necessarily a context-free language, but not necessarily a regular language. $L$ is necessarily a non-regular language. None of the above