Counting Deterministic Finite Automata I have a question regarding counting DFAs:


  Given a  Σ = {0, 1} input string, with the state set Q = {1...n}, how would I find the total number of DFAs that can be constructed?


I believe this is a combinatorics problem, but I am not really sure what I would have to multiply. 

Thanks.
This is indeed a nontrivial problem. A solution can be found in this paper: Enumeration and Random Generation of Accessible Automata.