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Communication Dans Un Congrès Année : 2001

Relating levels of the mu-calculus hierarchy and levels of the monadic hierachy

Résumé

As already known, the mu-calculus is as expressive as the bisimulation invariant fragment of monadic second order Logic (MSO). In this paper, we relate the expressiveness of levels of the fixpoint alternation depth hierarchy of the mu-calculus (the mu-calculus hierarchy) with the expressiveness of the bisimulation invariant fragment of levels of the monadic quantifiers alternation-depth hierarchy (the monadic hierarchy). From van Benthem's result, we know already that the fixpoint free fragment of the mu-calculus (i.e. polymodal Logic) is as expressive as the bisimulation invariant fragment of monadic Σ0 (i.e. first order logic). We show here that the ν-level (resp. the νμ-level) of the mu-calculus hierarchy is as expressive as the bisimulation invariant fragment of monadic Σ1 (resp. monadic Σ2) and we show that no other level Σk for k > 2 of the monadic hierarchy can be related similarly with any other level of the mu-calculus hierarchy. The possible inclusion of all the mu-calculus in some level Σk of the monadic hierarchy, for some k > 2, is also discussed.
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Dates et versions

hal-00659988 , version 1 (14-01-2012)

Identifiants

  • HAL Id : hal-00659988 , version 1

Citer

David Janin, Giacomo Lenzi. Relating levels of the mu-calculus hierarchy and levels of the monadic hierachy. LICS, 2001, Boston, United States. pp.347--356. ⟨hal-00659988⟩

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