158 questions linked to/from How to prove that a language is not regular?
16k 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 ...
7k 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 ...
7k 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?
3k 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 ...
2k views

### Prove that the following language is not regular: $\{0^i1^j : i \neq j\}$ [duplicate]

I was trying to approach this proof, after multiple reads and attempts I am getting nowhere. If someone could help me out that would be great. Should I use the pumping lemma, if so how show I start, ...
1k 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'...
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 ...
1k views

623 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 ...
978 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 ...
241 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 ...
784 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 language....
201 views

157 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 ...
122 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 ...
234 views

### Proving a language is non-regular using the Pumping Lemma for non-binary strings [duplicate]

I am unsure of how to prove this language is non-regular. I do not even know where to start to develop a string that would prove the language is non-regular by contradiction. Any help would be ...
181 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 ...
### Provide “regular” grammar for this language {${a^ib^j \mid i>0\ and \hspace{2.5mm}i\leq j \leq(2*i)}$} [duplicate]
I'm trying to understand the approach to constructing an grammar which accepts the language ${a^ib^j \mid i>0\ and \hspace{2.5mm}i\leq j \leq(2*i)}$ } Thanks.
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 ...