No, it is not.

You can invent a variety of notations to describe a DFA. But you can't change the formal definition of a DFA, or what kinds of things a DFA can match without making it not a DFA.

I'll say to you what I said above, but even moreso: Er... I'm not sure what you're saying here, so I'll clarify what I was saying. What I mean is, we all agree on what DFAs are, and so we all agree on what regular languages in the original, Kleene sense are. But once we start admitting non-regular languages into our notion of "regular expression" because they're "straightforwardly tacked on", it's unclear what the limits are supposed to be.

I'm not actually a fan of using "regular expressions" in a sense broader than that of Kleene's regular, DFA-accepted languages, to be clear. That is exactly what I've been questioning.

You can actually quite easily add features to regular expressions, that are typically excluded while still being actually regular. Examples would be an `and` or a `not` operator.

What I am saying is that you can come up with a lot of extensions of the basic regular expression language. But there is no subjectivity at all in whether the extensions can be implemented by a DFA. Either you can, or you can't.

Not really. A graph is either a valid DFA or it is not. At that point, it's a matter of tooling in terms of "straightforward"ness.

Er... I'm not sure what you're saying here, in that it doesn't seem to be engaging with what I was saying, or trying to say, so I'll clarify what I was saying. What I mean is, we all agree on what DFAs are, and so we all agree on what regular languages in the original, Kleene sense are. But once we start admitting non-regular languages into our notion of "regular expression" because they're "straightforwardly tacked on", it's unclear what the limits are supposed to be.

I'm not actually a fan of using "regular expressions" in a sense broader than that of Kleene's regular, DFA-accepted languages, to be clear. That is exactly what I've been questioning.

I think the intent of the parent comments was to say that it's fine to consider a regex a standard "regular expression" in the mathematical sense if it still translates to a DFA and matches a regular language. For instance, mathematical regular expressions typically only include '*' (0 or more), not '+' (1 or more). However, you can still translate a regex including '+' to a DFA. Likewise arbitrary repetition mechanisms like {m,n}, case-insensitivity, and other features that add convenience without actually matching non-regular languages.

On the other hand, backreferences can allow matching non-regular languages.

Ah, yeah, I see now that that is indeed probably what they meant; thanks! In that case, yes, I'm sympathetic to that, using regex to just mean "Anything that ultimately describes a regular language".

I don't think so, not too much anyway, I think the "software engineering" aspects of it would place reasonably strong constraints on what is desirable and on what is feasible (for a DFA). That's probably how the (informal?) consensus emerged.