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.
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
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?
@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.
I am stuck on the following question
If L is regular show that even(L) is also regular
where even(L) = {even(w) : w ∈ L}
w is a string in L
even(w) is the string obtained by extracting from w the letters in even numbered 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