Multi-Valued MSO Logics OverWords and Trees

Authors:
Manfred Droste;Werner Kuich;George Rahonis
Affiliations:
Institute of Computer Science, Leipzig University D-04009 Leipzig, Germany. E-mail: droste@informatik.uni-leipzig.de;Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien Wiedner Hauptstraße 8-10, A-1040 Wien, Austria. E-mail: kuich@tuwien.ac.at;(Correspd.) Department of Mathematics, Aristotle University of Thessaloniki 54124 Thessaloniki, Greece. E-mail: grahonis@math.auth.gr
Venue:
Fundamenta Informaticae
Year:
2008

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Abstract

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 ω-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.