## 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

tree automaton
Full Text:

### References:

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