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An initial semantics for the \(\mu\)-calculus on trees and Rabin’s complementation lemma. (English) Zbl 0873.68157

Summary: We show that the function associated with any closed or nonclosed term of the \(\mu\)-calculus on trees can be represented by a recognizable set of trees whose nodes are labeled by letters and by sets of variables. Rabin’s complementation lemma is an immediate consequence of this result.

MSC:

68R10 Graph theory (including graph drawing) in computer science
68Q45 Formal languages and automata

Keywords:

tree automaton
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