# Tagged Questions

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### Pumping Lemma & Regular Language

For each regular language L, we have an integer k such that: ...
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### 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 ...
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### 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
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### Systematic way of creating the complement of a regular grammar?

Regular languages are closed under complement. And any regular language can be generated using a regular grammar. Is there a systematic way to create the rewrite rules for the complement of a regular ...
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### A computer's memory is finite, so how can there be languages more powerful than regular?

A computer has a finite memory. There are no computers with infinite memory. Therefore the only languages that a computer can process are those whose member strings are finite. As I recall, the ...
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### Why do complex grammars require powerful algorithms?

I am reading a fabulous book on Formal Languages and in the book it says: As the rewrite rules of a grammar become more complex, the algorithm for recognizing the associated language becomes ...
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### Regular Functional Algorithms

A language is regular if it is accepted by a read-only Turing machine. I am curious about applying this model to functional problems rather than decision problems. Definition: A functional read-only ...
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### If $L\in REG$ then $M$ has a finite number of distinct rows

Let $L \subseteq \Sigma^{\star}$ and let $M^{\Sigma^{\star} \times \Sigma^{\star}}(\{0,1\})$ an infinite matrix such that for each $x,y\in \Sigma^\star$:  m_{x,y}=\begin{cases} 1 & x y\in L\\ 0 ...
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### Is the set of codes of Deterministic Finite-State Automata a regular language?

Let $\Sigma$ be a given alphabet. Is there a way to code up Deterministic Finite state Automata (DFA) over $\Sigma$ as strings of $\Sigma$ in such a way that the corresponding subset of $\Sigma^*$ is ...