A Medvedev Characterization of Recognizable Tree Series
We introduce representable tree series over commutative semirings, which extend representable sets  to the weighted setting. We prove that restricted representable tree series are exactly those tree series that can be recognized by weighted tree automata. Moreover, we investigate the relation between unrestricted representable tree series and weighted monadic second-order logic.
The author thanks Tobias Denkinger and Johannes Osterholzer for several useful discussions concerning the content of this work.
- 6.Droste, M., Götze, D., Märcker, S., Meinecke, I.: Weighted tree automata over valuation monoids and their characterization by weighted logics. In: Kuich, W., Rahonis, G. (eds.) Algebraic Foundations in Computer Science. LNCS, vol. 7020, pp. 30–55. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-24897-9_2 CrossRefGoogle Scholar
- 10.Medvedev, Y.T.: On the class of events representable in a finite automaton. Automata Studies (1956). Also in Sequential machines - Selected papers (translated from Russian), pp. 215–227. Addison-Wesley (1964)Google Scholar