# Tagged Questions

Regular expressions or Regex is a search pattern for strings defined by a sequence of characters.

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### Solving the equation X = AX + B of languages for X [duplicate]

I'm currently working on the following problem for my computer theory class. It goes as follows: Let $A$ and $B$ be regular expressions. Show then that $A^* B$ is the solution of $X = AX + B$. ...
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### Expression for a bounded function

I have a bounded function, $$y= \begin{cases} 1 & \text{if x>1} \\ x & \text{if 0\leq x\leq 1}\\ 0 &\text{if x < 0} \end{cases}$$ Does anyone ...
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### Regular Expression Proof

I am trying to prove the following statement: If $S$ and $T$ are any regular expressions over a 1-letter alphabet and if $n$ is a natural, then the languages $(ST)^n$ and $S^nT^n$ are equal.
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### Number of sequences that contain a given “run”

Consider sequences of numbers 0, 1, 2 with length n. There are $3^n$ such sequences. I want to know how many sequences there are that contain a k-run of 1's followed by 2. As a regular expression: ...
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### The number of elements in a set

I have a small task, part of my homework, which tends to confuse me because of its simplicity. It makes me think that I am missing something. I have to find the number of elements in the set {w | w ∈ ...
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### L is language generated by the context free grammar G = (V, $\Sigma$, P, S)

L is language generated by the context free grammar G = (V, $\Sigma$, P, S), where $\Sigma$ = {a,b,c}, V = {S, A, B}, and the production set P is: S -> aSb | A A -> cAb | B B -> cb My question is, ...
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### how to covert regular expression in simplest form?

I have made this expression from nfa (NFA to regular expression) : (a+ab+aa*b)*(a+a*a) but at book answers it is written like this : (a+aa*b)*(a*a) I am thinking that the my answer is same as book ...
I have the following language: L = {w $\in$ {a,b}* | aa is not part of w}. I have to construct a regular grammar from this language and I thought about first finding the regular expression from the ...