Proceedings ArticleDOI
Tree automata, mu-calculus and determinacy
E.A. Emerson,C.S. Jutla +1 more
- pp 368-377
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TLDR
It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees, which provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results.Abstract:
It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the mu-calculus, the equivalence provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results. It is also shown how mu-calculus can be used to establish determinacy of infinite games used in earlier proofs of complementation lemma, and certain games used in the theory of online algorithms. >read more
Citations
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References
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Journal ArticleDOI
Results on the propositional μ-calculus
TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
Book ChapterDOI
Automata on infinite objects
TL;DR: This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree.
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Descriptive Set Theory
TL;DR: Descriptive set theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets.
Journal ArticleDOI
Decidability of second-order theories and automata on infinite trees
TL;DR: In this article, it was shown that the second-order theory of countable linearly ordered sets is decidable, and that the theory of automata on infinite trees is also decidable.