Not long ago some of my roommates at my dorm invited me over for a dinner to their kitchen.

An hour or so into us enjoying our meal enjoying our meal a girl from China, who also happened to share the same kitchen entered, microwaved her food and was gone in 5 minutes without saying a word. 😶

Shortly thereafter, my dorm mates started chattering about how “rude” and impolite she was. They mentioned that they never spoke to each other, although they used the same kitchen.

Nonetheless I wasn’t convinced she was rude. Maybe she was just shy or…

During my previous semester at college I took a course on projective geometry, which is basically a “fancier” field of geometry. It’s most important property is that ratios do not change(stay invariant) under projective transformations and that parallel lines meet at a point at infinity.

Recently I stumbled upon an interesting conditional probability problem, that actually turned out to be a quite famous and well studied paradox.

Nevertheless, I still think it’s worth writing a short article on it and the solution. Besides, if you can’t teach it, you don’t understand it well enough.

Two children problem (boy-girl paradox)

Let’s say there is a couple that has 2 children, whose gender is either biological male m or female f. When you meet them they tell you that one of their children is a female f.

Now, like every other normal person, you immediately start asking yourself what the probability is…

Let’s say we have been given a DFA(Deterministic Finite Automaton), which accepts a certain language L consisting of words from the closure Σ* over an alphabet Σ.

Wow, that was a mouthful, but let’s start with a quick example.

For a given alphabet Σ = {a, b} we get the closure Σ* = {ε, a, b, aa, ab, ba, bb …}. The language L is then nothing more than a finite subset of that closure.

I assume the reader is familiar with the definitions of DFA, RegEx, etc.

Our task consists in converting the given DFA to a regular expression…

Valentin Matzke

Interested in difficult problems, long-term thinking, contrarianism, philosophy...striving to become an overman/uebermensch

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