@Evil huh, your code is running too fast?

I created a chat room dedicated to compilers, interpreters and programming languages for this website. The reason I didn't create it on SO it's because the main purpose of that chat room would be to discuss theories behind those topics (that is theories behind scanning, parsing, IRs, code generation, compilers vs interpreters, functional languages, etc), which are relatively important in computer science.

Here's the link to the chat.

An example of a question that could also be asked there, I think, would be: chat.stackexchange.com/transcript/message/37547660#37547660

Hello! I'm trying to prove that a;; regular languages $L \in \{a, b\}^*$, which characters indexed $0, 1, \ldots, n$ is still regular if all oddly-indexed characters are removed. I'm not sure which closure properties to use to try and demonstrate this

@AdamWilliams Hello!

Hi @nbro

Interesting problem

A frustrating one :P

I'm not really sure where to start.. one of the ideas I had was duplicating the original language NFA representation and trying all possible characters in $\sigma$ after reading one input character

But just to clarify, you're asked to prove that all languages which are formed from other regular languages by removing the oddly-indexed characters from all strings of those same languages are still regular, right?

Correct, yeah. For completeness, here's the original question lol768.com/i/xR.VV.y2.Fq.ek.wq.UE.8F

Hopefully I haven't butchered any of the original details by paraphrasing

Well, if you run the original FA, you can skip every odd position

so the original FA would accept or reject the new string

If I'm not wrong

so you'd need to bypass intermediate states?

i.e. you can create a FA which checks if you're in a odd or even position

Okay, that part seem straightforward

but I'm not completely sure... today I'm a little bit tired... lol

Maybe you should ping Gilles

If nothing else it's a better starting point than I had, I appreciate the thoughts :)

@Gilles any thoughts on this?

@AdamWilliams I actually found a question similar to yours, but except that instead of removing characters at odd position it's about removing characters at even positions.

@vzn nah, it is rather that way - you look at the watch, code for a while, realise it is a perfectly good moment to sleep, and the alarm clock shouts it isn'tz

oooh, thanks for that @nbro

I'll need to read up on the homomorphisms

second answer looks good though, sticks to principles I've learnt

To make you understand what's a homomorphism: a linear map/transformation (from linear algebra) is a homomorphism between vector spaces.

Depending on the underlying algebraic structure, you have different names for homomorphims