"buffalo" can function as a verb (bully) and a plural noun (bison).
So we can write "Bison bully bison." as "Buffalo buffalo buffalo."
I'm going to tag my groups of bison with numbers.
> Bison(1) bully bison(0).
> Buffalo(1) buffalo buffalo(0). (3 words)
Now, we can qualify bison(1), by stating that they are bullied by another group of bison, which I'll call bison(2). We can rewrite "who are bullied by bison(2)" as "bison(2) bully" (similar to rewriting "food that is liked by me" as "food I like") so we get:
> Bison(1) who are bullied by bison(2) bully, bison(0).
So that gives us sentences of lengths 3, 5, 7, 9, 11, ... words. We can add a word to each sentence by just adding the qualifier "Buffalo" (meaning "from the city of Buffalo") before buffalo(0). This gives us sentences of lengths 4, 6, 8, ...:
> Bison(1) bully bison(0) from the city of Buffalo.
So now we just need the sentences of lengths 1 and 2, which we can do by using the imperative. I.e. we give the general instruction "Bully." or the more specific instruction "Bully bison.":
> Buffalo. (1 word)
> Buffalo buffalo. (2 words)
The issue remains: can we call a sentence "valid" if it is entirely incomprehensible?
The sentence is nonsensical, because it refers to the same group three times - Bison from Buffalo. If bison from Buffalo bully other bison from Buffalo, it's tautological to again repeat the point that they bully bison from Buffalo.
You'd need more specific demographics to make the sentence valid, methinks, and when that happens, you're adding in a new word.
You're making the classic nerd error of assuming that natural languages should be as precisely defined as mathematics or computer languages. You're going to tell me that there's no such thing as deceleration next!
(To be fair, "Buffalo buffalo buffalo buffalo buffalo." isn't exactly a "natural" sentence.)
And in any case, the sentence is still syntactically valid, which is all I'm really concerned about here.
I'm not operating from logic, but from a 'natural' perspective. I've no problems with the syntax ("French citizens German citizens bully, bully Belgian citizens") though it's quite an awkward sentence in that format and any editor would require a rewrite, but it's just not something that someone would say if all the demographics were the same ("French citizens French citizens bully, bully French citizens") - ie, it's nonsense for that reason.
While the sentence is technically ambiguous, we say ambiguous things all the time and still manage to understand one another. This is the domain of the study of Pragmatics.
In natural communication, we START by assuming that the speaker had a meaningful intention, and then attempt to infer that meaning from context and assumptions about shared knowledge. I can easily think of contexts in which your "French citizens" sentence make sense.
"buffalo" can function as a verb (bully) and a plural noun (bison).
So we can write "Bison bully bison." as "Buffalo buffalo buffalo."
I'm going to tag my groups of bison with numbers.
> Bison(1) bully bison(0).
> Buffalo(1) buffalo buffalo(0). (3 words)
Now, we can qualify bison(1), by stating that they are bullied by another group of bison, which I'll call bison(2). We can rewrite "who are bullied by bison(2)" as "bison(2) bully" (similar to rewriting "food that is liked by me" as "food I like") so we get:
> Bison(1) who are bullied by bison(2) bully, bison(0).
> Buffalo(1) buffalo(2) buffalo buffalo buffalo(0). (5 words)
We can modify bison(2) in the same way we modified bison(1), by stating that they are bullied by yet another group of bison, called bison(3):
> Bison(1) bison(2) bison(3) bully bully bully bison(0).
> Buffalo(1) buffalo(2) buffalo(3) buffalo buffalo buffalo buffalo(0). (7 words)
And so on...
> Buffalo(1) buffalo(2) buffalo(3) buffalo(4) buffalo buffalo buffalo buffalo buffalo(0). (9 words)
> Buffalo(1) buffalo(2) buffalo(3) buffalo(4) buffalo(5) buffalo buffalo buffalo buffalo buffalo buffalo(0). (11 words)
So that gives us sentences of lengths 3, 5, 7, 9, 11, ... words. We can add a word to each sentence by just adding the qualifier "Buffalo" (meaning "from the city of Buffalo") before buffalo(0). This gives us sentences of lengths 4, 6, 8, ...:
> Bison(1) bully bison(0) from the city of Buffalo.
> Buffalo(1) buffalo Buffalo buffalo(0). (4 words)
> Buffalo(1) buffalo(2) buffalo buffalo Buffalo buffalo(0). (6 words)
> Buffalo(1) buffalo(2) buffalo(3) buffalo buffalo buffalo Buffalo buffalo(0). (8 words)
So now we just need the sentences of lengths 1 and 2, which we can do by using the imperative. I.e. we give the general instruction "Bully." or the more specific instruction "Bully bison.":
> Buffalo. (1 word)
> Buffalo buffalo. (2 words)
The issue remains: can we call a sentence "valid" if it is entirely incomprehensible?