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1answer
26 views

A CFG Grammar for One Language

Suppose : $w_1,w_2 \in \{a,b\}^∗$ and $ L=\{w_1w_2 \mid w_1,w_2 \in \{a,b\}^* \land n_a(w_1)=n_b(w_2)\}$ $n_a$ is number of $a$'s and $n_b$ is number of $b$'s. This is a Entrance Exam question. I ...
1
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1answer
54 views

Challenge on Property of Complement in Language

We have: and M be a finite automata. Suppose d(M) be a deterministic automata that equivalence to M. if $M_1$ and $M_2$ be two finite automata, $M_1 + M_2$ is the finite automata such that the ...
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0answers
25 views

Language of Specific Grammar

I ran into this exercise in Sipser's Note on Computation Theory. Consider the following grammar $G$: $$\begin{align} S &\to aSD \;|\; bB \\ D &\to dS \;|\; a \\ B &\to bB \;|\; ...
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0answers
35 views

Pumping Lemma & Regular Language

For each regular language L, we have an integer k such that: ...
0
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0answers
11 views

A name for the number system used in versioning software

Software often uses a numbering system where one "digit" increments independently of the others. For instance, the next version of Software 2.9 might be Software 3.0 or Software 2.10 or Software ...
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1answer
21 views

disproving union of infinitely many regular languages

I want to disprove the following statement: "if $L$ is the union of infinitely many regular languages, then $L$ is guaranteed to be a regular language." I don't know where to start. Any hint will be ...
2
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2answers
38 views

“The regular languages over $A$ are the homomorphic pre-images in $A^*$ of subsets of finite monoids.”

I'm trying to understand the statement: The regular languages over $A$ are the homomorphic pre-images in $A^∗$ of subsets of finite monoids. which appears in the Wikipedia article on free ...
0
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1answer
40 views

Pumping lemma proof of $L = \{a^nb^m \mid 0\leq n<m\}$

Prove the following language is not regular using the pummping lemma $L = \{a^nb^m \mid 0\leq n<m\}$ I tried solving this problem what I don't think I was able to reach an accurate proof. But this ...
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1answer
33 views

Frequency of Words in Document

I'm trying to figure this out: Would someone care to explain how one would go about using this function? More specifically, I don't understand the interval part, how does one count the intervals? ...
1
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2answers
31 views

NFA for $L = \{ w \in \{a,b,c\}^* : \text{at least one symbol appears only once in }w \}$

Write an NFA to recognize the language $$L = \{ w \in \{a,b,c\}^* : \text{at least one symbol appears only once in }w \}.$$ I'm not quite sure how to do this question. I don't know how to keep ...
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0answers
31 views

Pumping lemma for $a^n b^{2n}$

I have this question and i am not sure and trying to solve in both way that is through diagram and expression: Question : Prove that $a^nb^{2n}$ is not regular. contradiction: ...
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0answers
37 views

Proving irregularity using Myhill-Nerode theorem

I'm trying to prove that the following language is irregular using the Myhill-Nerode theorem $$ L = \{ w\space\epsilon \{a,b,c\}^* | \#_b(w) > (\#_a(w) + \#_c(w))! \} $$ While it's completely ...
0
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1answer
17 views

Prove that a language is not regular.

I want to ask how to prove the following language is not regular using closure properties. I tried to use pumping lemma but I find the proof itself shaky. I'd appreciate if you can help. The ...
1
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2answers
68 views

pumping lemma: ww^R not regular

I'm trying to prove that $L = \{ww^R : w \in \{a,b\}^*\}$ ($w^R$ is the reverse of $w$) is not regular using the pumping lemma. Let $p$ be the pumping length and $s = a^pbba^p$. $x = \epsilon$, $y = ...
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2answers
30 views

Can an infinite set of primes be a regular language or CFG?

At first glance, it seems like the pumping lemmas should somehow "easily" show that an infinite set of primes (say, written in binary) cannot be a regular language or context-free grammar. But I don't ...
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2answers
35 views

Gives regular expressions which defines regular language and what does {1,2} mean

The question is give a regular expression which defines a regular language. Question: The language over {0,1} consisting of all strings which either have length less than 3 or have 0 as their third ...
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1answer
15 views

Finding a Regular Expression with a Specific Length from a language

Given this language, I was supposed to find the Regular Expression that represented it. Having given up and getting the answer later (below) I couldn't understand the regular expression. Given ...
0
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2answers
24 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
41 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
65 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
26 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
18 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
28 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 ...
0
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1answer
30 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
34 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
37 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 ...
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0answers
30 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
32 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
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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
38 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 ...
1
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1answer
55 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
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3answers
54 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. $$L = \{ a^n b^n c^n \mid n \geq 0 \}.$$
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1answer
40 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
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1answer
60 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
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1answer
28 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 ...
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2answers
57 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 ...
1
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1answer
44 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
20 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
57 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
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1answer
24 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
36 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
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1answer
27 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
votes
1answer
22 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
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1answer
27 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: ...
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0answers
52 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. ...
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2answers
57 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 ...
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3answers
71 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 ...
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2answers
535 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 ...
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1answer
110 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 ...
3
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1answer
30 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 ...