Linked Questions

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1answer
10k views

Is this language regular or non-regular: {ww : w ∈ {a,b}* } [duplicate]

This is a question from a text book that's giving me some trouble. The question is: Determine whether or not this language is regular. Justify your answer. $$L = \{ww : w \in \{a,b\}^* \}$$ I ...
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1answer
5k 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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1answer
2k views

Proving that {0^{2^k}} is not regular with the Myhill-Nerode theorem [duplicate]

My language is the repetition of 0 to a length that's a power of 2: $L = \{ 0^k \ni k=2^n, n \geq 1 \}$ I want to know how to prove that this language is not regular. I have attempted the proof ...
2
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1answer
2k views

Show that a language consisting of strings of a prime number of 1s is irregular using pumping lemma [duplicate]

Question: L is a language defined as $\ L = \{1^l | l\in primes\}$ (strings of 1s having a prime length). Show that this is not a regular language ($\ L \notin REG$). You may either use the theory ...
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1answer
910 views

Union of finite and non-regular language [duplicate]

Question: ($B$ and $C$ are languages) $B$ is finite,$C$ isn't regular: Prove/Disprove: $C\cup B$ isn't regular. Thoughts: My intuition says this is true, but I need an idea to prove it. Since I don'...
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1answer
2k views

Prove that the language L = {a^(m+n) b^m a^n | m, n ≥ 0} ∪ {a^m b^n a^(m+n) | m, n ≥ 0} is not regular [duplicate]

In general, how can we go about proving that union of two languages as non regular. In this case, the individual languages can be proved as non regular using pumping lemma. How can we apply pumping ...
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2answers
888 views

Prove or disprove whether L is regular [duplicate]

Let $\Sigma = \{0,1\}$. For every word $w \in \Sigma^*$, let $|w|_0$ and $|w|_1$ denote the count of 0's and 1's, respectively, in $w$. Let $L$ be the language $$L = \{ w \in \Sigma^* \mid |w|_0 \gt |...
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1answer
990 views

pumping lemma for $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ [duplicate]

Using pumping lemma, how can I prove that $L=\{a^n b^m c^k \mid n = m \vee m\neq k\}$ is not regular?. If I choose $w= a^m b^m c^m$ and pump up with $i=2$, if have $a^m=1 b^m c^m$ but the string is ...
1
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1answer
436 views

Non-regular Languages? [duplicate]

Possible Duplicate: How to prove that a language is not regular? Why $L_a$ and $L_b$ are not reguluar? $L_a = \{ e^i f^{n-i} g^j h^{n-j} : n \in N, 1 \leq i, j \leq n \}$. $L_b= \{nm^{i_1} ...
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2answers
483 views

L ={ $a^{m^n}$ | $m$>$n$ } is Regular or not by pumping Lemma [duplicate]

L ={ $a^{m^n}$ | $m$>$n$ } I am bit confuse whether to consider this language as L = $(a^{m})^{n}$ OR L = $a^{\left(m^n\right)}$. If it is considered as L = $(a^m)^{n}$ then want to check it ...
1
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1answer
774 views

Proving a language is not regular [duplicate]

I need to prove that the following language is not regular $\{c^mb^na^n \mid n>0,m\geq0\}$ But I am not sure how to do that for this particular one. I vaguely understand pumping lemma, but ...
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2answers
272 views

Finding nfa or dfa for a language [duplicate]

I'm trying to study for the summer ahead of class I saw this question, please how do I go about it? Find NFA/DFA for the language $L = \{0^n1^n : n \in N\}$
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1answer
699 views

Pumping lemma on {a^n | n=3^k} — help finishing the proof [duplicate]

I am working on a pumping lemma question and trying to prove that the following is not regular, but I can't finish the proof, if someone can help me it will be great. So I am given this language: $L ...
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1answer
801 views

Using the pumping lemma for a proof by contradiction [duplicate]

I'm trying to prove that the set of even-length strings with the two middle symbols being equal cannot be accepted by finite automata. I can explain why it cannot be accepted intuitively, but I'm ...
2
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2answers
103 views

Class of a Language [duplicate]

What are the common ways to check if a given language is regular, context free, or context sensitive? Any surveys or notes would also be helpful. There's no need to describe your suggestions. eg. it ...
3
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1answer
166 views

How to prove for that a given non-regular language its given super-set is also non-regular? [duplicate]

Consider the non-regular language $L_1$ = {$a^n$b$a^n$: $n \geq 0$} and its super-set language L = Language of strings with equal number of trailing and leading a's, or in other words, $$L = \{a^...
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1answer
393 views

Proving that a language given by a CFG is not regular [duplicate]

Consider the language defined by the following grammar: $$ \begin{align*} &S \rightarrow E \\ &S \rightarrow \epsilon \\ &E \rightarrow E+E \\ &E \rightarrow E-E \\ &E \rightarrow \...
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1answer
367 views

Proving a grammar/language as not regular [duplicate]

$D → T ∨ D | T$ $T → C ∧ T | C$ $C → ¬C | name | ( D )$ $name → a | b | c | d$ I am not looking for the complete answer, but more the methodology of working this out. How would I go about proving ...
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1answer
264 views

Show this language is non-regular using pumping lemma: B = {ww | w ∈ {a,b,c,…,z)*} [duplicate]

The question I'm working from is: Prove whether or not a finite automation exists that recognises the following language: B = {ww | w ∈ {a,b,c,...,z)*} EDIT So I believe this is a non-regular ...
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1answer
148 views

Proving a language is not a regular language but a context free language [duplicate]

I have the languages $L_1$ and $L_2$ such that $L_1 = \{a^nba^n :n \in N\}$ and $L_2 =\{a,b\}^*\setminus L_1$. I want to prove that $L_2$ is not a regular language. I know that to prove that $L_2$ is ...
1
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1answer
284 views

proving {$a^ib^jc^k : j = i \lor j = k$} is not regular [duplicate]

i had troubles proving this is not regular using the pumping lemma {$a^ib^jc^k : j = i \lor j = k$}. Not sure how to approach this anymore, and help would be appreciated
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1answer
113 views

Showing that $\{ c^n a^m b^{n+m} : n+m \geq 6\}$ is not regular [duplicate]

I'm trying to show that $L_6=\{c^n a^m b^p : n+m=p,p \geq 6\}$ is not regular. I need a little help, I was practicing the pumping lemma, and I encountered this language, I saw these conditions and got ...
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2answers
129 views

How to prove that these two languages are regular, or not regular? [duplicate]

I have these two languages $L_1={\{a^n b^m,n≥m+5,m>0}\}$ Where $∑=(a,b)$ $L_2={\{a^n b^m,n≥m+5,m≤5}\}$ Where $∑=(a,b)$ As you can see that there is only one difference, the condition of ...
0
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1answer
94 views

Prove this language is non-regular [duplicate]

I'm struggling to understand this question using pumping lemma to prove a language is not regular. Any help would be appreciated. Prove using the Pumping Lemma that the following language is not ...
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3answers
175 views

Irregularity of language of words whose length is of power of 2 [duplicate]

How to show that the language containing the words whose length is a power of $2$, $L=\{w\mid|w|=2^i\}$, isn't regular using the pumping lemma? The pumping lemma says that Let be M a regular ...
2
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1answer
100 views

How to prove that $L_1=1^*\cup \{0^i 1^{j^2}|i\ge 0,j\ge 0\} $ is irregular? [duplicate]

We know that $L=\{0^i 1^{j^2}|i> 0,j\ge 0\} $ is irregular (by the Pumping Lemma), we have to use it to prove two things: $L_1=1^*\cup \{0^i 1^{j^2}|i\ge 0,j\ge 0\} $ is irregular. $L_1$ is ...
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1answer
119 views

Why are these languages not regular? [duplicate]

Show that the following languages are not regular: $(1)\ L=\left\{a^nb^mc^k\mid n>k \land n,m,k>0\right\}$ $(2)\ L=\left\{a^nb^mc^k\mid m>k \land n,m,k>0\right\}$ I've difficulties ...
1
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1answer
138 views

How to show that $L=\{ wa^kw | w \in \{ a,b,c \}^* ,k \geq 0 \}$ is not regular using the pumping lemma for regular languages? [duplicate]

I'm trying to show that the language in the title is not regular but I don't know how to chose a decomposition $x = abc$ to express the word in the language because the $w \in \{a,b,c\}^*$ is kinda ...
1
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2answers
75 views

Prove that a language is not regular with process of elimination [duplicate]

When deterministic automaton, I need to prove that you can't implement the language in it, because the language is not regular. Easiest way to prove that a language is regular, is just by making an ...
0
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1answer
122 views

Pumping lemma not regular [duplicate]

How would about proving this is not regular with the pumping lemma. Please include all steps and explain all steps. I am really new with this. $1^{2x}0^y$ and $y>= x$ Does it matter which side ...

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