The power of first-order quantification over states in branching and linear time temporal logics

Chatterjee, Krishnendu; Dasgupta, Pallab; Chakrabarti, P. P.

doi:10.1016/j.ipl.2004.05.003

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“…In [RP03], quantification is expressed as taking a synchronized product with a labelling automaton. Finally, quantification over states (rather than over atomic propositions) is studied in [PBD + 02, CDC04], where model checking is proved PSPACE-complete (both for branching-time and for linear-time).…”

Section: Introductionmentioning

confidence: 99%

Quantified CTL: Expressiveness and Complexity

Laroussinie¹,

Markey²

2014

Logical Methods in Computer Science

104

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Abstract. While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic Second-Order Logic for both semantics) and characterise the complexity of its model-checking and satisfiability problems, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy).

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Section: Introductionmentioning

confidence: 99%