Tagged Questions

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Prove that the language is not regular without using Pumping Lemma

I am practising problems on Regular Languages and I came across this question: Prove that the language $$\{a^m b^n : m ≥ 0, n ≥ 0, m \ne n\}$$ is not regular. (Using the pumping lemma for this ...
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Clearing a Confusion regarding the Proof of equal no of a's and b's not being a regular language

I was wondering about its proof. The direct use of pumping lemma here is not a viability. So a certain teacher of mine proved this with the notion that $a^{n}b^{n}$ being a subset of this language ...
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Unable to understand an inequality in an application of the pumping lemma for context-free languages

The problem Prove that the language $\qquad L = \{a^n b^j \mid n = j^2\}$ is not context free using pumping lemma. Approach taken by the book To prove such statements, the book takes the ...
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CFL, pumping lemma

I have difficulty with proving that the language $L = \{ a^p b^q | p \ge 1 , q \ge 1 , p \ge q^2 \vee q \ge p^2\}$ $w = uvxyz$ I've chosen word $w = a^{N^2} b^N$ where $N$ is a constant ...
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Using the Pumping Lemma to show that the language $a^n b a^n$ is not regular

I've seen a lot couple of questions regarding the pumping lemma that are pretty similar to each other and this one is unfortunately not the exception. Most likely will be this question marked as a ...
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Regular language not accepted by DFA having at most three states

Describe a regular language that cannot be accepted by any DFA that has only three states. I'm not really sure where to start on this and was wondering if someone could give me some tips or ...
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How can both |y| = 0 and y⁰ = ε hold in the Pumping lemma?

There is something in the pumping lemma that I do not quite understand, namely if $s$ is at least of length $p$, then we could split it to $xyz$ such that the following conditions are met: For each ...
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Is this the correct way to use the pumping lemma?

I've been watching lectures from Coderisland on YouTube about finite state machines, DFAs and NFAs, and in one discussion he talks about how to use the pumping lemma to show how a language is not ...
127 views

Proof that {$a^m b^n$ | m!=n} is not regular [duplicate]

I know that the language $\{a^m b^n | n\neq m\}$ satisfies the pumping lemma, but it's still not regular (I have to count the # of a's and b's). How can I formally prove it?
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Is the following language context-free? $L= \{a^nb^m| m\geq2^n\}$

Is $L=\{a^nb^m|m\geq2^n\}$ a context-free language?
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Is L= $\{ww \mid w \in \{a,b\}^*\}$ context-free? [closed]

Let $L = \{ww \mid w \in \{a,b\}^*\}$. In other words, each word of $L$ is some string repeated twice (some string concatenated with itself). Is the language $L$ context-free?
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Context free language and the complement of it

Given the language $L_1 = \{a^i b^j c^k \mid i \neq j \vee i \neq k\}$, I need to determine whether it is context-free by using the pumping lemma. I must do the same for the complement of this ...
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Using pumping lemma to prove a language is not context free

When using the pumping lemma for a context free language, if I write any $w \in L$ as $uvxyz$, is my goal to show that a string will not pump for ANY arrangement of $uvxyz$ that I choose, or is my ...
38 views

Pumping a Language does not imply regular [duplicate]

I am currently studying the pumping lemma for regular languages and I am trying to come up with an example where even if the language can be pumped it is not regular. Which condition of the lemma ...
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Decide if L is regular or not and argue it. Trying to use Pumping Lemma

Part (a): Let $L = \{x \in \{0,1\}^* \mid \#0(x) \neq 4\times\#1(x)\}$, where $\#0(x)$ means the number of 0 in string $x$ and $\#1(x)$ means the number of 1 in string $x$. So I want to use the ...
57 views

Concatenation among different language types

I am trying to figure out the result of the concatenation among different language types (regular, context free, ...). I think the result strongly depends on the nature of the languages which will be ...
789 views

Is the language that accepts strings concatenated with their reverse regular?

If the set of regular languages is closed under the concatenation operation and is also closed under the reverse operation ($x^R$ is the reverse of $x$) then is the language generated by ...
175 views

Is $L = \{a^jb^ia^{j-i}\mid i,j \ge 0\ , j > i\}$ context-free?

I'm exercising for an upcoming exam and I find this exercise: Say whether or not the language $$L = \{a^jb^ia^{j-i}\mid i,j \ge 0\ , j > i\}$$ is a context-free language. Justify your ...
277 views

Is the language of words containing equal number of 001 and 100 regular?

I was wondering when languages which contained the same number of instances of two substrings would be regular. I know that the language containing equal number of 1s and 0s is not regular, but is a ...
831 views

Example of a non-context free language that nonetheless CAN be pumped?

So basically L satisfies the conditions of the pumping lemma for CFL's but is not a CFL (that is possible according to the definition of the lemma).
169 views

Is {xyx | |x|≥1} context-free?

Is $L=\{ xyx \mid x,y \in \{a,b\}^* \text {and } |x| \ge 1 \}$ context-free? If yes, please explain how we can write grammar or create a PDA for it. If not a CFL, then prove it through pumping ...
821 views

Is this strange language context free?

Is the following language context free: $L = \{ uxvy \mid u,v,x,y \in \{ 0,1 \}^+, |u| = |v|, u \neq v, |x| = |y|, x \neq y\}$ ? I think that it's not context free but I'm having a hard time proving ...
171 views

Prove that context free languages are not closed under swapping prefixes and suffixes

Prove that context free languages aren't closed under this operation: $A(L) = \{ zyx \mid x,y,z \in \{0,1 \}^*, xyz \in L \}$ Obviously, we need to find a context free language $L$ such that $A(L)$ ...
254 views

Is the language $L = \{ a^ib^j \mid i\ \nmid\ j \ \}$ context free?

Is the language $L = \{ a^ib^j \mid i\ \nmid\ j \ \}$ context free ? If we fix $n \in N$ then we know that the language $L = \{ a^ib^j \mid \ \forall \ 1 \le k \le n \ , \ \ j\neq ki \}$ is ...
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Is pumping lemma for regular languages “closed” against Kleene star?

If I have an infinite language $L$ which fulfills the Pumping lemma for regular languages, does $L^*$ also fulfill the same conditions?
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Prove that $\{0^n 1^{n\cdot m} : n,m \in \mathbb{N}\}$ is not context-free

This is a homework problem I have spent several hours on. A "hint" is given that we may use this fact: If $n,j,k \in \mathbb{N}$ satisfy $n \geq 2$ and $1 \leq j+k \leq n$, then $n^2+j$ does not ...
144 views

Where do the length restrictions of the pumping lemma come from?

For a language $L$ with pumping length $p$, and a string $s\in L$, the pumping lemmas are as follows: Regular version: If $|s| \geq p$, then $s$ can be written as $xyz$, satisfying the following ...
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How to feel intuitively that a language is regular

Given a language $L= \{a^n b^n c^n\}$, how can I say directly, without looking at production rules, that this language is not regular? I could use pumping lemma but some guys are saying just looking ...
149 views

Length of mid part of the string in Pumping Lemma

This standard definition of pumping lemma from Wikipedia. Let $L$ be a regular language. Then there exists an integer $p\ge 1$ (depending only on $L$) such that every string $w$ in $L$ of length ...
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Show that a language is not regular using the Pumping Lemma [duplicate]

Possible Duplicate: How to prove that a language is not regular? Given a language $L = \{a^pb^{2p} \mid p \ge 1\}$, how could I show, using the Pumping Lemma that $L$ is not regular?
There is a problem which I cannot solve. If you give a tip I will be very glad. Prove that following language is not context free: $L= \{ a^nb^m | \gcd(n,m) = 1 \}$. It can be proven using the ...