Feasible computation through model theory
Feasible computation through model theory
The expressive power of finitely many generalized quantifiers
Information and Computation
Information and Computation
On the expressive power of variable-confined logics
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Ordering Finite Variable Types with Generalized Quantifiers
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
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We show that there is a class C of finite structures and a PTIME quantifier Q such that (1) IFP(Q) is bounded on C but L∞,ωω(Q) ≠ PFP(Q) ≠ IFP(Q) = FO(Q) over C. (2) For all k ≥ 2, IFPk(Q) is bounded but not uniformly bounded over C. (IFPk(Q) denotes the k-variable fragment of IFP(Q)) (3) For all k ≥ 2, IFPk(Q) is not uniformly bounded over C but IFPk(Q) = Lk(Q) over C.