fsa: compleixity and frequency

Suppose we list all the finite state automata (FSA) up to a certain size.
The size of a FSA is the number of states in an automata.
Many of the FSA can be shown to be equivalent (i.e. there are many FSA which accept a given language).

Let us define the complexity of a language as the size of the smallest FSA that accepts that language and only that language.

My hypothesis is that, a less complex language will have many FSA that can recognize it than a more complex language.
In other words, a complex language will not be represented very frequently in the list of FSA up to a certain size. And a simple language will be represented more frequently.

Is there any work on this?

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Thanks,

John Woodward

http://www.cs.bham.ac.uk/~jrw
mobile 07740867560 Office (tel) 0121 414 8808.  (fax) 0121 414 4281
School of Computer Science The University of Birmingham B15 2TT UK
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