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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.enter image description here

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!

Words of the same length in a language

Let $LsubseteqSigma^*$ be a language, where $Sigma$ is a set, and let $ninmathbb N$.

I am wondering if there is some good terminology for

$LcapSigma^n$.

Of course I could say “the set of words in $L$ of length $n$” but maybe there is some special terminology like “level set of length”, “grade”, “homogeneous section” or I don’t know what…. ?

discrete mathematics – Probability: portion of wrong and correct words edited by proofreader

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google sheets – How to combine words from multiple cells with the REGEXMATCH command?

I am a beginner with google sheets.

I want for exemple use the REGEXMATCH command to recognize when certain combinations of words is found in a specific cell,for exemple: =REGEXMATCH(C25;C29&D15)

Let’s say that in C25 there is the text “I like blue apples.”
In C29 I have the text “blue” and in D15 “apples”. Ok, it is TRUE.

But let’s say that I also have a C30 with the word “green” and D16 with the word “bananas”.

And I want the =REGEXMATCH(C25;C29&D15) to also include combinations of “blue bananas” or “green apples” and so on if I write these combinations in C25. How do I write the code to accomplish this?

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