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Multi-Valued MSO Logics Over Words and Trees

Droste M., Kuich W., Rahonis G.

Fundamenta Informaticae

2008

Vol. 84, nr 3-4

305-327

We introduce multi-valued Büchi and Muller automata over distributive lattices and a multi-valued MSO logic for infinite words. For this logic, we prove the expressive equivalence of w-recognizable and MSO-definable infinitary formal power series over distributive lattices with negation function. Then we consider multi-valued Muller tree automata and a multi-valued MSO logic for trees over distributive lattices. For this logic, we establish a version of Rabin's theorem for infinitary tree series.