Expressive Completeness for LTL With Modulo Counting and Group Quantifiers

Expressive Completeness for LTL With Modulo Counting and Group Quantifiers

Kamp showed that linear temporal logic is expressively complete for first order logic over words. We give a Gabbay style proof to show that linear temporal logic extended with modulo counting and group quantifiers (introduced by Baziramwabo,McKenzie,Thérien) is expressively complete for first order logic with modulo counting (introduced by Straubing, Thérien, Thomas) and group quantifiers (intr...

On Presburger Arithmetic Extended with Modulo Counting Quantifiers

We consider Presburger arithmetic (PA) extended with modulo counting quantifiers. We show that its complexity is essentially the same as that of PA, i.e., we give a doubly exponential space bound. This is done by giving and analysing a quantifier elimination procedure similar to Reddy and Loveland’s procedure for PA. We also show that the complexity of the automata-based decision procedure for ...

Constraint Satisfaction with Counting Quantifiers

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers ∃ which assert the existence of at least j elements such that the ensuing property holds. These are natural variants of CSPs in the mould of quantified CSPs (QCSPs). Namely, ∃ := ∃ and ∃ := ∀ (for the domain of size n) We observe that a single counting quantifier ∃ strictly between ∃ and ∀ a...

On the locality of arb-invariant first-order formulas with modulo counting quantifiers

We study Gaifman locality and Hanf locality of an extension of first-order logic with modulo p counting quantifiers (FO+MODp, for short) with arbitrary numerical predicates. We require that the validity of formulas is independent of the particular interpretation of the numerical predicates and refer to such formulas as arb-invariant formulas. This paper gives a detailed picture of locality and ...

Correspondence and Completeness for Generalized Quantifiers