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.
-
(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))
-
(3)
For all k ≥ 2, IFP k(Q) is not uniformly bounded over C but IFP k(Q) = L k(Q) over C.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Dawar. Feasible Computation through Model Theory. PhD thesis, University of Pennsylvania, Philadelphia, 1993.
A. Dawar and L. Hella. The expressive power of finitely many generalized quantifiers. Information and Computation, 123(2):172–184, 1995.
A. Dawar, L. Hella, and A. Seth. Ordering finite variable types with generalized quantifiers. In Thirteenth Annual IEEE Symposium on Logic in Computer Science, 1998.
H. Ebbinghaus and J. Flum. Finite Model Theory. Perspectives in Mathematical Logic. Springer, 1995.
Y. Gurevich, N. Immerman, and S. Shelah. Mccolm’s conjectures. In Ninth Annual IEEE Symposium on Logic in Computer Science, pages 10–19, 1994.
Y. Gurevich and S. Shelah. Fixed-point extensions of first-order logic. Annals of Pure and Applied Logic, 32:265–280, 1986.
L. Hella. Logical hierarchies in PTIME. Information and Computation, 129:1–19, 1996.
P. G. Kolaitis and M. Y. Vardi. Fixpoint logic vs. infinitary logic in finite model theory. In Seventh Annual IEEE Symposium on Logic in Computer Science, pages 46–57, 1992.
P. G. Kolaitis and M. Y. Vardi. On the expressive power of variable confined logics. In Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 348–359, 1996.
G. L. McColm. When is arithmetic possible? Annals of Pure and Applied Logic, 50:29–51, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-46674-6_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66856-5
Online ISBN: 978-3-540-46674-1
eBook Packages: Springer Book Archive