Abstract
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 ω∞ , ω(Q) ≠ IFP(Q) = FO(Q) over C.
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(2)
For all k ≥ 2, IFP k(Q) is bounded but not uniformly bounded over C. (IFP k(Q) denotes the k-variable fragment of IFP(Q))
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(3)
For all k ≥ 2, IFP k(Q) is not uniformly bounded over C but IFP k(Q) = L k(Q) over C.
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Seth, A. (1999). On L k(Q) Types and Boundedness of IFP(Q) on Finite Structures. In: Thiagarajan, P.S., Yap, R. (eds) Advances in Computing Science — ASIAN’99. ASIAN 1999. Lecture Notes in Computer Science, vol 1742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46674-6_28
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DOI: https://doi.org/10.1007/3-540-46674-6_28
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