## Articles For More Creative Brains Follow Annahme 5 Steps in german 1200 words for \$15

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## Explaining NFA in words

I have an NFA, and the question I am asked is :

Let 𝑎 < 𝑏 < 𝑐. Now in simple English, express the language of the NFA to explain what type of strings are accepted by it.

In simple English, my answer is

The NFA accepts strings over alphabet {a, b, c} such that the last symbol appears twice.

Which I know is correct, however my problem lies in the question where "a < b < c". How does this affect my NFA and is my answer still correct? My answer seems really short for 6 marks.

## Finite automaton for all words whose length \$n\$ satisfies \$operatorname{gcd}(n,504) geq 6\$

I have been working on the following homework question, and I just can’t seem to make any progress:

Construct a finite automaton having fewer than 36 states that recognizes the language $${s in a^* : operatorname{gcd}(|s|, 504) geq 6}$$, where $$|s|$$ is the length of $$s$$.

So far I have been trying to figure out a regular pattern in $$504$$ and have broken it down to the prime factorization $$504 = 2^3 cdot 3^2 cdot 7$$, which means that all divisors must be multiples of 2, 3, or 7. However I don’t know how to create the finite automaton (NFA or DFA). Any help is appreciated!

## In LibreOffice, how to ignore spell checking words containing a period (like stackexchange.com)?

Out of the box, LibreOffice’s spell-checker successfully ignores strings like `stackexchange_com`, but it marks strings like `stackexchange.com` as spelling errors.

How does one configure LirbreOffice to ignore spell-checking strings with a period in them, like `stackexchange.com`? Please note that I do not use AutoCorrect to convert these strings into hyperlinks, nor do I want to do that.

## passwords – In Hashcat, How to generate combinatior attacks consisting of more than two words (in lenght)?

I am trying to make a combinator attack using just one dictionary:

``````word1
word2
word3
word4
word5
...
``````

And would like to try all 4-words-length permutations separated by commas:

``````word1,word2,word3,word4
word1,word3,word4,word2
word2,word3,word6,word1
...
``````

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## Is the language of words that contain a square regular or context-free?

A word is square-free if it contains no non-empty sub word of the form $$y^2$$. Your language consists of all words over $${a,b}$$ which are not square-free. It is not difficult to enumerate (using exhaustive search) all square-free words over $${a,b}$$:
$$epsilon, a, b, ab, ba, aba, bab.$$
Since this list is finite, the language of square-free words over $${a,b}$$ is trivially regular, and so is its complement.

In contrast, the language of square-free words over $${a,b,c}$$ is not regular. This follows from the existence of an infinite square-free word $$w$$, which can be obtained from the Thue–Morse sequence.

Indeed, I claim that the set of prefixes of $$w$$ is pairwise inequivalent modulo your language. To see this, let $$x,y$$ be two such prefixes, say $$x$$ is a prefix of $$y$$. Then $$y = xz$$, and so $$xz$$ is square-free while $$yz = xz^2$$ isn’t.

Alternatively, we can apply the pumping lemma to the language of all square-free words over $${a,b,c}$$. If the pumping length is $$n$$, take the prefix of $$w$$ of length $$n$$, and pump it up so that it contains a square. Similarly, since the Thue–Morse sequence is an infinite binary cube-free sequence, the language of cube-free words over $${a,b}$$ is not regular.

The latter argument shows that the language of square-free words over $${a,b,c}$$ and the language of cube-free words over $${a,b}$$ are not context-free. This leaves the following questions open:

1. Is the language of non-square-free words over $${a,b,c}$$ context-free?
2. Is the language of non-cube-free words over $${a,b}$$ context-free?