I'm currently studying compilers and am having some issues with understanding regular sets. For example, lets say I had a set of binary strings, (0, 1). Would all integers that are even and positive be considered part of a regular set? Lets say I have that same set, but instead of being even, they are divisible by 5, would it still be a regular set?
I've been looking at this helpful guide I found online, but I'm still confused about what can be defined as a regular set.
Would all integers that are even and positive be considered part of a regular set?
Yep! You can generate them with this regular expression:
2 | 4 | 6 | 8 | (0|1|2|3|4|5|6|7|8|9)+(0|2|4|6|8)
Lets say I have that same set, but instead of being even, they are divisible by 5, would it still be a regular set?
Yep! Here's the regex:
5 | (0|1|2|3|4|5|6|7|8|9)+(0|5)
More generally, to determine whether a set is a regular set, you should try to find a finite automaton that accepts precisely the strings in the language or a regular expression for that set. If you can do that, the language is regular. If not, it's not regular.
Hope this helps!