[seqfan] Re: A new sequence counting the number of distinct languages recognized by DFAs

[brad klee]

> A129622 might be number of minimal DFAs of n states up to equivalence,
> with equivalence meaning same language accepted. 

Nice find, thanks, we should have seen that much earlier. It matches 
the differences of terms calculated so far (as expected). 

So... The other proposal--is there a better way of grading the base 
binary regex function space or is 2 x A091147 good enough? 

On one hand, it's annoying to have ((X|Y)|Z) and (X|(Y|Z)) instead 
of (X|Y|Z), which would appear one level sooner. 

On the other hand, allowing n-ary combinators makes the recursive 
enumerator much more complicated, to the point where I wouldn't 
expect a nice generating function (haven't checked though).  

Would also be nice to find a mapping between function compositions 
and {H,Ux4,D} words. HH=a* and UD=(a|(a|b))+(a(a|b)) are vaguely 
understandable at first. Then HHH=a**, and three ways to insert 
a star: HUD, UHD, UDH, okay. This is still far from a proof...  

(see also: http://list.seqfan.eu/pipermail/seqfan/2024-July/075176.html )



--Brad