Regular languages are formal languages which are recognized by a finite automaton. It is equivalently the languages which are expressible as a regular expression. In addition to these two, there are several other equivalent definitions.
Questions tagged [regular-language]
1253 questions
7
votes
4 answers
Determine if a language is regular from the first sight
Is there a way to guess if a language is regular from the first sight? I.e. in order to choose proof methods, I have to have some hypothesis at first. Do you know any hints/patterns?
I need this to reduce time consumption: for instance, in order not…
petajamaja
- 271
4
votes
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Applying the Myhill-Nerode Theorem
Consider the language $$L=\{x y^{(n)} z y^{(n)} w: x,z,w \in \Sigma^*, y \in \Sigma, z\text{ does not contain }y, n \geq 0 \}.$$
To show that the language is not regular using the Myhill-Nerode Theorem, I have to show that there are infinite number…
evinda
- 7,823
4
votes
1 answer
Possible solution for Sipser 1.63
Sipser's question 1.63:
Let A be an infinite regular language. Prove that A can be split into two
infinite disjoint regular subsets.
Is my solution correct?
Since $A$ is infinite and regular, then the pumping lemma holds. We have a pumping length…
TheNotMe
- 4,841
4
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0 answers
Pumping lemma for $a^nb^{2n+1}$
I know how to solve pumping lemma for $a^nb^n:n\geq 0$.
But I don't understand how can I solve this example : $a^nb^{2n+1}:n\geq 0$.
I tried to solve it but I am not sure that I have solved it correctly or not?Could somebody please help me here?
I…
user2342605
- 41
4
votes
2 answers
Language with error.
Let $L \subset \{0, 1\}^∗$ be regular language.
$$L_e = \{ w | w = uxv, x \in \{0, 1\}, u\overline{x}v \in L\}$$, where $\overline{x} = 1 − x$
Prove $L_e$ is regular language.
For example: If $10 \in L$, then $11, 00 \in L_e$ $.
I am thinking…
user180834
- 1,453
3
votes
1 answer
How do you prove that the set of neighbors of $L$ is regular if $L$ is regular?
I know that a regular language can be made into a DFA, so can I just make a DFA for the regular language? Also, someone told me I should make a e-NFA from the DFA, but I don't see what would be the point. I was at one of the tutorial and the…
george
- 33
3
votes
1 answer
Show that the class of regular languages is closed under gapping
"Let $\Sigma=\{a, b\} . $ For every word $ w=a_{1} \ldots a_{n} \in \Sigma^{*} $ with $ a_{i} \in \Sigma $ and $ 1 \leq k \leq n $ let $ w_{k}^{-}:=a_{1} \ldots a_{k-1} \overline{a_{k}} a_{k+1} \ldots a_{n} $, while $ \overline{a_{k}} $ is the…
iina
- 39
3
votes
2 answers
Is $\frac12 L$ a regular language?
Let $L$ be a regular language. Is $\frac{1}{2}L := \left\{ w: \exists_u |u|=|w| \wedge wu\in L \right\}$ regular too?
I think the answer is YES. But I don't know how to prove it. I was trying to modify finite state machine for $L$ to accept…
xan
- 2,053
3
votes
1 answer
Pumping lemma and $L \subset \{a\}^*$
Let $L \subset \{a\}^*$ and $L$ satisfies pump lemma. Prove that $L$ is regular.
Please help me.
My an attempt:
Definition. A language $L$ of $A^∗$ is recognized by a monoid $M$ if there is a monoid morphism11 $f:A^* \rightarrow M$ and a subset $X$…
user180834
- 1,453
3
votes
1 answer
Regular languages- homomorphism.
Let $h: \{ a,b,c,d \}^* \rightarrow \{a,b\}^* $ be a homomorphism such, that
$h(a) = aa, h(b) = ab, h(c) = ba, h(d) = b $ . Determine:
$h^{-1}((bab)^*ba^*b).$
I have trying do it by 4 hours. I don't have idea. I observed, what is obvious,…
user180834
- 1,453
2
votes
1 answer
Regularity of "middles" of words from regular language
I need some help with the following problem: $L$ - regular language and i have to prove that the language $P$ = {$\alpha$| $\beta\alpha\gamma \in L$, $\beta,\gamma \in (A)^*$} is regular. In other words $P$ is the language of all parts of words from…
user54060
- 43
2
votes
2 answers
Why is $S(L)$ regular?
Let $L$ be a regular language, and $\Sigma$ be its alphabet. Then, the language $S(L) = \{y \in \Sigma^*~|~xy \in L \text{ for some string }x \in \Sigma^*\}$ is also regular.
I am trying to demonstrate this by constructing a Non-deterministic Finite…
John Hoffman
- 2,734
2
votes
2 answers
Is $L = \{\omega : \omega\text{ contains exactly one 'foobar'}\}$ regular?
Is the language $L = \{\omega : \omega\text{ contains exactly one 'foobar'}\}$ regular? I have a hunch that it is non-regular because a regular expression representing the language must remember that is has encountered the substring…
David Faux
- 3,425
2
votes
1 answer
Can a non regular language be a subset of a regular language
If I have a Language A and A is not regular and A is a subset of B, then B can't be regular.
I think this is False. Because I can have
B = {a^m b^n | m,n >= 0}
A = {a^m b^m | m >=0 }
A is not regular and B is regular. And A is a subset of B. So it…
penatozawa
- 23
2
votes
2 answers
Proving that a certain language is regular
Consider two languages $L$ and $\operatorname{minimum}(L) = \{ w \in \Sigma^* \mid w \in L, \text{ but no real prefix of $w$ is in $L$}\}$.
I want to prove now, that for every DFA language $L$ , minimum(L) is a DFA language too.
First thought:…
letter
- 43