# Tagged Questions

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### Smallest grammar problem on a single character.

Let the alphabet be $\Sigma = \{a\}$. Say $s = a^6 = aaa aaa$. If the repeated variable $A = aa$ appears $k$ times in the expanded starting rule of a smallest grammar $G_s$ for $s$. Then that ...
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### The max number of repeats of substrings of a sample of a language.

So we suspect that finding the smallest grammar of strings in the language $\{a^n : n \in \Bbb{N}\}$, is hard. But luckily as far as applications to natural language processing, we would rarely ...
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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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### Context free grammar $L=\{a^ib^jc^k|j=i+k-2\}$

$L=\{a^ib^jc^k|j=i+k-2\}$ This expression surprise me a lot and put me into deep thinking. what i am doing by solving the expressions: ...
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### There is a sequence of operations on grammars of a string that strictly decreases the size of grammars down to the smallest grammer.

I'm trying to figure out the smallest grammar problem, which yes I know is impossible since it's such a hard problem, but humor me for a sec. Let $g$ be a smallest grammar for the string $s$ over the ...
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### Palindromes with 2 symbols and $3|l(u)$

The following grammar generates palindromes with 2 symbols. $$G=\{\{S\}, \{a,b\}, \{S\rightarrow\epsilon|a|b|aa|bb|aSa|bSb\}, S\}$$ So if I'm right, each $u$ in the language $L$ generated by $G$ is a ...
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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 ...