Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The modal mu-calculus alternation hierarchy is strict
Theoretical Computer Science
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Games and Model Checking for Guarded Logics
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
A Hierarchy Theorem for the µ-Calculus
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
On the Variable Hierarchy of the Modal µ-Calculus
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
On Observing Nondeterminism and Concurrency
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Undirected graphs of entanglement 2
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
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The modal μ-calculus Lμ attains high expressive power by extending basic modal logic with monadic variables and binding them to extremal fixed points of definable operators. The number of variables occurring in a formula provides a relevant measure of its conceptual complexity. In a previous paper with Erich Grädel we have shown, for the existential fragment of Lμ , that this conceptual complexity is also reflected in an increase of semantic complexity, by providing examples of existential formulae with k variables that are not equivalent to any existential formula with fewer than k variables. In this paper, we prove an existential preservation theorem for the family of Lμ-formulae over at most k variables that define simulation closures of finite strongly connected structures. Since hard formulae for the level k of the existential hierarchy belong to this family, it follows that the bounded variable fragments of the full modal μ-calculus form a hierarchy of strictly increasing expressive power.