Mealy-Moore machine book recommendation

Question

I've been researching Mealy and Moore machines for quite some time but it seems to me like there is a lack of good books/articles on the topic. All the research in this area seems to be mainly focused on two aspects: modeling sequential circuits and training probabilistic transducers. I see there is almost no research that would deeply investigate computational and algebraic properties. Is there a Chomsky hierarchy of Mealy machines? Is there a pumping lemma or Myhill-Nerode theorem for Mealy machines? Is Kleene algebra still applicable (and if so, then maybe it has some special new features)? Is there something like "rational relations", which would be the counterpart to rational languages?

Any materials would be greatly appreciated!

Answer 1

You should read:

• Finite-State Techniques Automata, Transducers and Bimachines by Stoyan Mihov - this contains all the basic information about transducers
• Automata, Languages and Machines by Eilenberg - it has information about rational relations
• Handbook of Weighted Automata by Droste - it goes one step further and introduces theory of weighted automata