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

[brad klee]

> I would appreciate it if someone could independently check my 
> values (maybe some existing library related to DFAs could be used).

Arthur makes a good point--It would be easier to help if you 
could explain more the details of your schema and algorithms. 

Is it essentially just a problem of enumerating labeled graphs 
and checking equivalences? If yes, can you specify exactly what 
the atoms and rules are for building the labeled graphs? 

For example, we can see that what Arthur says about the n=1 case
is true just by noting that there is only one transition graph 
with all edges tied down, thus leaving only one degree of freedom,
whether the start node is encircled as accepting or not. 

It sounds like what you've done is to allow free-floating edges 
that are assumed as pointing to rejections? Or perhaps instead
of free-floating edges, you've omitted them entirely?  

Meanwhile, it's nice for QA purposes if you can say things like 
"every state has exactly two outputs, every edge is between one 
or two states".   

Another thing that could possibly help... Do you have example 
drawings of the state transition diagrams at least in the 
smallest n=1 case? It would also be helpful to see examples 
when two (or more) drawings recognize the same language.  

Even if someone here is an expert in this field, you still 
might need to start by over-explaining yourself. This is 
actually a graphical subject area, so you're potentially 
missing an audience if you don't draw any diagrams. 

I'm not an expert, but given more details, it's potentially of 
interest for me to verify a few terms at least. We've done 
some things recently about making DFAs from FSMs, and your 
question seems relevant to that. 



Thanks,



--Brad