# Tagged Questions

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### 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 ...
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### 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 ...
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### Finding regular expressions

I'm given the DFA shown below and need to find regular expressions for the following languages: $L_{1,2}^0, L_{2,1}^6, L_{2,5}^4, L_{2,3}^5, L_{1,3}^5$. The language $L_{p,q}^r$ is defined as ...
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### Constructing a Turing decidable machine from DFA

I am a trying to prove that every regular language is decidable. So in order to prove that I am trying to show that I can move from deterministic finite automaton (DFA) to a Turing decidable machine. ...
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### Working with the word w⋅y, while given the word y⋅w

$L$ is a regular language. I am given $F(L)$ such that $$F(L)= \{wy \mid yw\in L\}$$ I need to prove that if $L$ belongs to $L_\text{dfa}$, $F(L)$ also belongs to $L_\text{dfa}$. I am having a hard ...
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### Constructing a finite automata from a subset of its language

I am attempting to solve the following problem: Let $M=(Q,\Sigma,\delta,q_0,F)$ be a deterministic finite automata which accepts $L(M)$, and let $E$ be the subset of $L(M)$ consisting of all words of ...
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### Prove that if $L$ is a regular language over the alphabet $Z = \{ 0,1 \}$, then $L' = \{ax \mid x \in L \}$ is also regular for any a in $Z$.

Prove that if $L$ is a regular language over the alphabet $Z = \{0,1\}$, then $L' = \{ax \mid x \in L\}$ is also regular for any $a \in Z$. I'm not sure how to even begin on this one. If even a ...
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### Basic regular expressions problem

I'm in an intro to CS theory class learning about regular expressions. I was wondering if people could give me hints as to whether I'm on the right track for these problems. I hope this particular ...
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### How to prove by pumping lemma these languages are not regular?

$L_1 = (a^k * b^r \mid k \neq r^2)$ $L_2 = (a ^{\sum_i ^n t} \mid n > 0 )$
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### Building a regular grammar from NFA

I'm requested to make a regular grammar from a given NFA. In this NFA, there's a "death state", which means, when getting to it, there's no way back to the rest of the states (a self-loop to the same ...
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### Proving or disproving regularity of a language

The question is as follows: If L1 and L2 are not regular and L1 ⊆ L ⊆ L2, then L is regular My intuition says that it's wrong so I've been looking for a ...
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### Homework proof Extended Transition Function by mathematical induction

Let M = (Q,∑, q0,A, δ) be an FA. Below are other conceivable methods of defining the extended transition function δ∗. In each case, determine whether it is in fact a valid definition of a function on ...
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### Existence of NFA for this language

I'm given a task to find (and prove) such language $L$ in the alphabet $\Sigma = \{a,b\}$ with all words less than $1000$ in length, for which any DFA/NFA will have more than $10^{10}$ of states. For ...
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### Creating a regular grammar

Hi I am trying to write a grammar for $L=\{xcy \mid x \neq y^R \land x,y \in \{a,b\}^*\}$. I am not able to think beyond a point as to how to write the grammar. Could someone guide me?
I'm taking a course on formal languages and was given this exercise: Give an algorithm to tell whether a regular language $L$ contains at least $100$ strings. Can someone give me a hint? Thanks! ...