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2answers
22 views

Why cant this be a Regular Language?

Given L - the language consisting of all the strings of the form $\{0^n 1 ^m\}$ where $m < n$ How can I prove that L is not a regular language?
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2answers
33 views

Regular Expressions Help [duplicate]

I need a little help with Regular Expressions. The allowed operations are obviously + (union) , * (Kleene star) and concatenation. I have to write Regex for the following 2 examples. I have tried a ...
1
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2answers
56 views

Formal Languages - Regular Expression

I've been battling the following two questions for more than a day today. Write a regular expression (comprised of {a, b}) that contain at least two b and do not contain abb. Write a regular ...
1
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2answers
20 views

FSM to be regular with atleast two 0's and at most two 1's

Is it possible to construct a FSM to prove that the set $X$ is regular, where $$ X = \{s \in \{0,1\}^* \mid \text{$s$ contains at least two $0$'s and at most two $1$'s}\}\ ? $$
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0answers
10 views

Hierarchy of hardness for the pumping lemma for regular languages.

Whenever I bring up the Pumping lemma for regular languages people often say `better to use the Myhill-Nerode theorem'. I want to make this thought rigorous. Def: A language $L$ is pumpable if there ...
0
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1answer
21 views

Prove a language is Context Free

I am working on the following problem and I do make a little progress. Let me state the question first: Prove that the set of strings consisting of $a$'s and $b$'s with an equal number of $a$'s and ...
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1answer
21 views

Can any Language that is generated LL1 Grammar is regular.?

I have a question is every language generated by LL(1) grammar is regular? I know that every regular language can be generated by LL(1) grammar.
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2answers
32 views

Closed regular languages

Are regular languages closed under the following construction? $f(L) = \{w \mid w \in L$ and for all prefixes $x$ of $w$ it holds that $x \notin L$ $\}$
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0answers
28 views

Minimal DFA for a given regular expression

How can I construct a minimal DFA from the following definition? $L=\{w \in \{a,b,c\}^* $: if the second-to-last letter from w is an $a$, then the number of $c$'s $\le 1\}$ I've already made a ...
0
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0answers
27 views

Context-free languages

Is the following language context-free? $\{ w \in \{a,b,c\}^* : (\#_a(w) - \#_b(w)) \cdot \#_c(w) = \#_b(w)$ and all c's are encountered before any a$\}$. $\#_a(w)$ = amount of a's in w Thanks in ...
1
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1answer
23 views

Is there a prefix-free regular language whose set of proper prefixes is not regular

Is there a regular language $L$ such that the language $$L^\prime := \{ w : w\text{ is a proper prefix of a word in }L \}$$ has the following properties: $L^\prime$ is not regular, and $L^\prime$ ...
1
vote
1answer
22 views

Subset of regular languages

Assume $L_1$ and $L_2$ two regular languages, and $L_1\subseteq L\subseteq L_2$. Does this imply that $L$ is a regular language? Thanks in advance.
1
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1answer
31 views

Name for grammars with rules $A \to uA$

Recall that a right-linear grammar is a grammar that consists of rules of the form $A\to uB$, where $A$ and $B$ are non-terminals and $u$ is a (possibly empty) word of terminals. Similarly for ...
0
votes
1answer
33 views

Prove or disprove whether the following is a regular language

I'm given the regular language L, and w being an element of L. If we remove the w from the language L, will the resulting language be still regular? Well I thought to be true. Since initially is a ...
1
vote
3answers
46 views

Prove that this language is not regular (Pumping Lemma)

Prove that the following language is not regular. I have no clue where to start. $$L = \{ a^n b^n c^n \mid n \geq 0 \}.$$
1
vote
1answer
37 views

Is $L=\{w\mid \text{ same number of 010 and 101}\}$ regular?

I tried to prove that this language is regular using NFA or regular expressions and didn't succeed. I would like to see some solutions
0
votes
1answer
36 views

Prove or disprove that the language $L_1 = \{a^nb^m \mid n < m \}$ is regular

I have possible strategy for a proof that it is not regular. I am wondering if it is valid. Step 1: Prove that the language $L_2 = \{a^nb^n\}$ is not regular (for example with the Pumping Lemma). ...
0
votes
1answer
18 views

Prove L is not a regular language (A Finite State Automaton cannot accept it)

$$\mathscr L = \{x \in \{0,1\}^* \mid \text{there is a } y \in \{0,1\}^* \text{ such that } x = yy\}$$ How can I prove that this is not a Regular language? I tried using proof by contradiction but ...
1
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2answers
33 views

How to solve pumping lemma questions?

I am trying to prove that L = { aNbMaN-M|N>=M>=0} is not regular using the pumping lemma. I am pretty confused how to solve this. What I have so far (which I am not sure is right) is: Assume L is ...
0
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1answer
37 views

Checking some Regular Expression problems

I'm given the alphabet $$ \Sigma = {\{a,b}\} $$ I tried to write a regular expressions for presenting the following sets: All strings in $$\Sigma ^ *$$ with: a-) number of 2s divisible by 4 b-) ...
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1answer
17 views

How to prove the following related with regular languages

How can we prove the following. If $$\sum$$ is any alphabet and L is any language $$L \subset \sum*$$ Then L*L* = L* ?
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0answers
52 views

Prove the following by using mathematical induction

If we define the alphabet such that $$ \Sigma = {\{a,b}\} $$ and let $w$ be a string over it. I'd like to prove $$ ( \operatorname{comp}(w))^R = \operatorname{comp}(w^R) $$ where $$ w^R$$ and ...
0
votes
1answer
20 views

Question about Notation in a Regular Language

I am a little confused about the following notation: $L' = \{xy|x\in L \ , y\in L^R\}$. I think this expression is not equivalent with palindrome but I am not entirely sure. For example, I think the ...
1
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2answers
26 views

Prove by induction on a string

I want to practice proving the following: Given a binary string s, I want to prove $s$ has the same number of substrings 01 and 10 $\iff$ the first and last character of $s$ is the same. For ...
2
votes
1answer
20 views

Equivalence of two regular expression

I have a quick question to ask. So I am trying to come up with a regular epxression which represent a language over {a,b} that contains at least one 'b' in it. I came up with this: $$(a| b)^*b(a| ...
0
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1answer
20 views

How can I show ithat a language is regular?

I have a very quick question about regular languages, I think $\{a^{2n}| n\geq 1\}$ is regular. I do know that pumping lemma can be used to show something that is not regular. I am wondering what ...
0
votes
1answer
22 views

Question About Pumping Lemma used on a FA

I am learning about pumping lemma and I am trying to solve a problem. I need to use pumping lemma to show that: the Language L(M) defined by the following machine is infinite. Here is the dfa: ...
2
votes
0answers
50 views

This proof in my textbook involving the pumping lemma appears incorrect - is it?

It states Let $B$ be the language $\{0^n1^n2^n | n \geq 0\}$. We use the pumping lemma to prove that $B$ is not regular. The proof is by contradiction. Assume to the contrary that $B$ is regular. ...
0
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2answers
39 views

Regex for strings with at least three unique characters

I'm trying to represent some string conditions in terms of regex. One of those conditions I find hard to transform is that the string must have at least three different characters. So is there any ...
3
votes
3answers
62 views

Is $L = \{(x,y,z) | x+y=z\}$ a regular language?

Suppose $x,y,z$ are coded as decimal or their binary representations in an appropriate DFA. Is $L$ regular? My intuition tells me that the answer is no, because there are infinitely many combinations ...
0
votes
2answers
167 views

Regex for strings with no three identical consecutive characters

I wanna ask what the regular expression for the strings having the property in the title should be. For binary string with no three consecutive 0, it's quite a simple regex ...
0
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1answer
33 views

Complement of a regular expression?

What is the regex for the complement of $r = b^*(ab + a^* + abb(b^+))^*$ ? I am thinking $(a+b)^*(abb)^+a^* $ since anything that contains $abb$ and is not followed by $b$'s would not be accepted ...
2
votes
1answer
28 views

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 ...
0
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0answers
44 views

“Whether the intersection of two regular languages is infinite” decidable or undecidable?

Could someone explain the below problem? "Whether the intersection of two regular languages is infinite" decidable or undecidable ? Regards Avisingh05
2
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1answer
34 views

Proof of Equivalence of NFA and DFA, quick question about the setup

I am looking at the proof of equivalence of non determinstic finite automata(NFA) and deterministc finite automata(DFA). I am have a small quesion about the construction: Let ...
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1answer
45 views

Pumping Lemma for regular languages proof template

http://www.cs.uiuc.edu/class/fa06/cs273/Lectures/pumping-lemma/pumping-lemma.html So, I went to that site and it says: $w = xyz$ $|xy| \leq p$ $|y| \geq 1$ for all $i$, $xy^iz$ is in ...
0
votes
1answer
179 views

Show that two disjoint languages are not separable

What is the general method to show that two disjoint languages are not separable? As an example, suppose we have: $A = \{\langle M \rangle : M ( \langle M \rangle )$ halts and says ACCEPT$\}$ $B = ...
0
votes
1answer
25 views

showing language that is non-regular using pumping lemma

I am looking over pumping lemma and the author is using it to show that the language is non-regular. {a^n b^n a^n} = {aba aabbaa aaabbbaaa........} Is there ...
0
votes
1answer
28 views

Struggling with Proof Writing. Simple question for demostration.

I am practicing writing proofs over regular expressions. Here is the question: Show that $(r\cup \varepsilon)^*= r^*$, where $r$ is a string. Intuitively, the left hand side is the concatenation of ...
1
vote
1answer
22 views

Give a regular expression for $A = \{1^{k}y|k \geq 1, y \in \{0,1\}^{*}$ and $y$ contains at least $k$ $1$'s $\}$

The regular expression that is given is $1(0 \cup 1)^{*}10^{*}$. I'm having trouble realizing why this regular expression describes the language given. For example, the string (for $k$ = 4) $1111$ ...
0
votes
2answers
101 views

Prove the language $\{a^k b^l : k \neq l \}$ is not regular

Prove that the following language is not regular: $$L=\{a^k b^l : k,l \ge0, k\ne l\}$$ The problem is that I should use "distinguished states" not the pumping lemma, which is usually used for such ...
1
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1answer
34 views

Regular languages and intersection

Let L be a language and R an infinite regular one. If L intersection R is a regular language, then L is a regular one too?
1
vote
1answer
39 views

Question about equlaity of two language, simple but tricky.

I found the following question tricky: If $A$ is a language, when will $A^*=A^+$? By definition, $$A^* = \bigcup^{\infty}_{i=0}A^i = A^0 \cup A^1 \cup A^2 \cup \cdots$$ $$A^+ = ...
1
vote
2answers
19 views

A question about operations on languages.

I come across this problem on a book. It states that: for languages A and B, $(A\cup B)^* = (A^*B^*)^*$. I know that the definition of star closure is $\left(\bigcup^{\infty}_{i=1}\right)A^i$. But so ...
2
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1answer
33 views

A correct proof for this pumping lemma example?

Given the language $L = \{0^{2^n} | n \geq 1\}$ So, the language contains all strings that have $2^n$ $0$s. First of all I take $z = a^{2^p}$ where $p$ is the constant guaranteed by the pumping ...
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1answer
17 views

Is the language regular or contextfree?

Could you tell me if the language $$L=\{ w \in \{a,b,c\}^*: $$$$\text{there is at least one time the substring abc and none of the symbols a,b,c is repeated three times} \}$$ is regular or ...
1
vote
1answer
17 views

Use closure properties for the language $L=\{a^kb^l:|k-l| \leq 100 \}$

Given the language $$L=\{a^kb^l:|k-l| \leq 100 \}$$ I have to show that $L$ is regular or context free using closure properties. I have done the following: The language is regular. Let $k>l$, then ...
1
vote
1answer
20 views

How can I show that the language is regular using the closure properties?

How can I show that the language $L=\{ w \in \{a,b\}^*: \text{ the word w contains an even number of a and an odd number of b} \}$ is regular using the closure properties?
1
vote
1answer
29 views

Pumping Lemma Squares Proof Explanation

I'm looking for some help understand this perfect squares proof using the pumping lemma. Here is the proof: I don't understand how n^2 + k < n^2 + n towards the end of the proof. Would anyone ...
0
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2answers
212 views

Regular expression and DFA/NFA questions

If a language L is generated by a regular expression, then L is recognized by a DFA. I think this is true, because regular expressions describe regular languages, those of which are exactly ...