# Tagged Questions

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### Regular Language and Unknown Operation

I read the $L$ is a Regular language. Define $L'$ as following: $$L'=\{a_2a_1a_4a_3\ldots a_{2n}a_{2n-1}\mid a_1a_2\ldots a_{2n} \in L\}.$$ why $L'$ is Regular? any hint or idea would be highly ...
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### Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
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### 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 ...
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### 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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### NFA from grammar productions

Based on this grammar: \begin{align} G = (\{S,A,B\}, \{a,b, c\}, S, P) \end{align} \begin{matrix} \\P: \\S → abaS | cA \\A → bA | cB | aa \\B → bB | cA | bb \end{matrix} I created this NFA: ...
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### Right-linear grammar from regular expression

I made a right-linear grammar that from this regular expression: The alphabet is: $Σ = \{a, b, c\}$ Regular expression: $r = cc^*(ba)^*bb$ My solution, it seems a little too short like I'm ...
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### NFA from regular expression

I'm trying to make an NFA from the following regular expression. I'm not sure about the edges between nodes $q2$ and $q4$, maybe someone can point out where everything went wrong.
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### Constructing regular grammar

I'm trying to make a regular grammar for this language: $$L = \{ a^ncb^m(cc)^p : n\ge 1, m\le 1, p\ge 0\}$$ Where the alphabet is $\Sigma = \{a,b,c\}$ It seemed like right-linear. This may be ...
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### Understanding how to convert a PDA to a CFG

Given a PDA, initialized with $\#$ on the stack, and with accepting states $q_a, q_b, q_c$ and the following transitions: (current state, stack head, input character, replacement for old stack head, ...