**1.001 regular-languages questions.**

Let $R$ be a regular set over the alphabet $\{0, 1\}$. Give a machine construction to prove that the set obtained by deleting one 1 from each even length block of 1’s is also regular, and using ...

I need help with proving the following language is not regular:
$$
L = \{ a^n b^k \mid n > k \} \cup \{ a^n b^k \mid n \neq k-1 \}
$$
My usual methods using pumping lemma are not getting me ...

I had an exam on Theory of Computation, and one of the questions was to write down a regular expression for the language over $\{0,1\}$ consisting of all words containing at least one 1. My answer was:...

Do i need the $*$ after the first $B$ in this regular expression $(B^* + C)^*$ ?
Do i need the $+$ after the first $B$ in this $\omega$-regular expression $(B^+ + C)^\omega$
Stated differently: Is $(...

I'm trying to find the w-regular language of this NBA. In 'Principle of Model Checking' - Book there's an algorithm for this problem:
1. Take the NBA as NFA and create the regular language to get from ...

I am currently solving a problem in which we have to show that we can not prove using pumping lemma that the language mentioned in the question is not regular.Here is the full question
Consider the ...

Given an NFA with alphabet $\Sigma = \{a, b, c\}$ defined in the diagram, is there a way to efficiently convert it into a regular expression?
The way I solved this problem is to first convert the NFA ...

I have no idea how to approach this problem, could I get at least a hint on how to go about proving/disproving this?
I've tried the pumping lemma but I don't think it applies here. I've also tried ...

For example, I have an NFA $A_n$ with alphabet $\Sigma = \{0, 1\}$.
The language recognized by this NFA is known to be $\{u1v\ |\ u, v \in \Sigma^*, |v| = n − 1\}$.
I was unable to get the ...

I have the language $$L = \{a^mb^nc^o| \, m + n + o > 5\}$$
where $m,n,o$ are non-negative integers.
I have to find whether the language is regular or not.
My attempt:
I feel it should be non ...

Tha class of regular lanugage is closed under the union operation.
If $A_1$ and $A_2$ are regular languages, then so is $A_1 \cup A_2$.
Thus, there are two finite automatons(FAs) $M_1$ and $M_2$ ...

I have to tackle this problem:
I have some strings that are my training set. These strings belong to a regular language corresponding to a deterministic finite automata (hidden namely I don't now it, ...

I have started to learn automata theory and languages. I am new to regular expressions.
As a use case in real world, I would like to construct a regular expression to accept a c-style string: ...

Firstly it's not a homework question secondly I find hard to use mathematics on stack exchange so I uploaded a photo of my query. Well I tried my best so you can understand, if not let me know

I know all the regular languages are decidable but not sure whether it can be done in LogSpace.

For two words $w,v \in\{0,1\}^*$ of equal lenght, let $w+v \in\{0,1,2\}^*$ denote the word in which the $i$-th word is the sum of $i$-th position of $w$ and $v$, as follows: if $w=a_1 \ldots a_n$ and $...

I am trying to complete this question. However, I am unsure of the steps necessary to complete the conversion from a CFL to a deterministic PDA.
I know that $ww' | w \in \left \{ a,b \right \}^{*}, w'...

I am working on an assignment where one of the sub questions is:
Let $A$ and $B$ be languages. Suppose $A$ is context free and $A ≤_m B$, which means that there is a computable function $f\colon \...

Setting:
regular expressions with backreferences
unary language (1-symbol alphabet)
Is the following problem decidable in this setting:
Given a regular expression with backreferences, does it ...

The language of a DFA can be the empty set (by defining no final states), but can a Regular Expression do that?
If Regular Expression cannot do that, does it mean that DFA and Regular Expression are ...

I am studying pumping lemma from Introduction to theory of computation by Michael Sipser. I wanted to check if the language generated by regular expression
...

I have an assignment that I have to do and the question is
Draw a DPDA that accepts the language L = {ba(bb)^(n+1)a^(n – 1) |n > 1}.
Im not looking for the answer but rather some direction. I ...

I was wondering, since $a^*$ is itself a star-free language, is there a regular language that is not a star-free language? Could you give an example?
(from wikipdia) Lawson defines star-free ...

The symmetric difference of $L_1$ and $L_2$ is defined to be: $(L_1-L_2) \cup (L_2-L_1)$.
Problem: I’m trying to prove that given L a non regular language and F a finite language there symmetric ...

How to prove using pumping lemma {0^n OR 1^2n OR 2^3n | n >= 0} is not context free
This isnt the same language as {0^n1^2n2^3n | n >= 0} as this language the numbers need to be in order.

How can I prove this identity of languages?
My aproach is the following:
Let A, B and C to be languages, and let x to be an arbitrary string.
(A ∪ B) ⇒ x ∈ A ∨ x ∈ B
How do you proceed?

Is it possible to define a 《chess language》:
language={alphabet = {(chess pieces, squares of chess board)}, grammar={rules of movement of pieces over the board}}?
I looked online but I cannot find a ...

Lets say we have $L_1$ which contains all binary numbers divisivle by 2 but not by 4. I would say this language contains all words with a 10 at the end. Ive found a regular grammar $G$ with $L(G) = ...

How can I create a context free grammar for the language $\{p^2q^mpr^nq^{2n+m}| m,n \ge 0\}$, where $\Sigma = \{p,q,r\}$?

I learnt Ardens theorem and its usage as follows:
Ardens Theorem
Let $P$ and $Q$ be two regular expressions over alphabet $Σ$. If $P$
does not contain null string, then $R = Q + RP$ has a ...

I came across following problem:
Suppose $L_1$ and $L_2$ are two languages, $M$ is a Turing machine
$L_1 =\{M|M$ accepts at most 2016 strings$\}$
$L_2=\{M|M$ accepts at least 2016 strings$\}$
...

The given description of language is:
$\Sigma=\{a,b\}$ and $L=\{a^nwa^n:n\geq 1,w\in\Sigma^*\}$
I felt its regular as we can always interpret $aabaa$ in string $aaabaaa$ as $w$. That is we can ...

Yes, this is a quiz question. It's from a self-paced course, but the answer just isn't correct to me no matter how I look at it. There isn't really an active community to consult.
My Regular ...

I came across problem asking whether given statement is true and false. The statement given was as follows:
Every Type-2 grammar can generate regular language.
I felt that Type-2 grammar means, ...

We know that $L=\{0^{m^2}\mid m\geq 3 \}$ is not a regular language. However $L^*$ is regular because we can generate $0^{120}$ to $0^{128}$ by some concatenations and then any other power of $0$ can ...

What is language of repeat(L) = {ww | w ∊ L} ?
My try:
I know it {ww | w ∊ (a,b)*} is context sensitive language. Here , what is meant by "repeat(L)" ? Can you explain it ? It is not a homework ...

This was a question that I got while taking a test at our university. The question paper was taken away after the exams. I remember the question only, not the multiple choices.
If a regular ...

I was solving this question:
Which of the following statement(s) is/are false?
$L^0=\{\epsilon\}$
$|L^0|=0$
The answer given was None. That is, none of these statements are false and ...

I am aware of following two facts related to two concepts: regular languages and finite sets:
Regular languages are not closed under subset and proper subset operations.
It is decidable ...

I'm a bit new to automata theory, I'm sorry if this question is a bit too simple. If this question has been answered somewhere already, please point me to it.
One basic problem I wanted to solve was ...

How can we make a DFA for given condition in title from alphabets {0,1} (binary).
What can be the regular expression for this?
My calculated expression is (a+b)*a(a+b)(a+b) , please correct me if i'...

What is nature of difference of regular language and context free language?
My guess is RL - CFL = RL
CFL - RL = CFLAm I correct with this?

I stumble across this problem:
Give right linear grammar.
The solution given was simple:
$S\rightarrow bA$
$S\rightarrow aS$
$A\rightarrow \lambda$
$B\rightarrow bA$
$A\rightarrow aB$
Earlier ...

Let L be a regular language.
Then $\Sigma^{*} \backslash L^{*} = (\Sigma^{*} \backslash L)^{*}$
How do I prove it is wrong?

How can I show that every context-free language over a unary alphabet is regular?

Basically what the title says. Why can you "ignore" the "xy" part if you want to prove whether a language is regular?

in my practice for a test I came across this question:
prove or disprove that those languages are regular:
I succeeded proving that the second language is nonregular with homomorphism but i'm having ...

There is a grammar G given: S->XaX
X->aX|bX|epsI just replied to the first question that was ...

Let $A$ be a pushdown automata with input alphabet $\Sigma$ and stack alphabet $\Gamma$ and let $R \subseteq \Gamma^∗$ be a regular language. Let $L_R(A) \subseteq \Sigma^∗$ be a language of such ...

I know that each regular language can be generated by a CFG.
This makes, in one sense at least: context-free languages more general than regular languages.
Are there known results about the '...

- formal-languages
- finite-automata
- regular-expressions
- automata
- pumping-lemma
- context-free
- closure-properties
- formal-grammars
- proof-techniques
- computability
- turing-machines
- algorithms
- complexity-theory
- pushdown-automata
- terminology
- decision-problem
- reference-request
- nondeterminism
- undecidability
- parsers
- compilers
- check-my-answer
- combinatorics
- notation
- time-complexity

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