Abstract
Motivated by computer science challenges, we suggest to extend the approach and methods of finite model theory beyond finite structures.
Partially supported by NSF grant CCR 92-04742 and ONR grant N00014-94-1-1182.
Preview
Unable to display preview. Download preview PDF.
References
S. Abiteboul, R. Hull and V. Vianu, Foundations of Databases, Addison Wesley (1994).
S. Abiteboul and V. Vianu, Generic Computation and Its Complexity, Proceedings of 23rd ACM Symposium on Theory of Computing (1991), 209–219.
L. Adleman and K. Manders, Computational complexity of decision problems for polynomials, Proceedings of 16th IEEE Symposium on Foundations of Computer Science (1975), 169–177.
L. Adleman and K. Manders, Diophantine Complexity, Proceedings of 17th IEEE Symposium on Foundations of Computer Science (1976), 81–88.
S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy, Proof verification and intractability of approximation problems, Proceedings of 33rd IEEE Symposium on Foundations of Computer Science (1992), 210–214.
J. Barwise, On Moschovakis closure ordinals, Journal of Symbolic Logic 42 (1977), 292–296.
L. Blum, M. Shub, S. Smale, On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines, Bull. Amer. Math. Soc.21 (1989), 1–46.
E. Börger, Annotated Bibliography on Evolving Algebras, in: E. Börger (Ed.), Specification and Validation Methods, Oxford University Press, to appear.
J. Cai, M. FĂ¼rer and N. Immerman, An Optimal Lower Bound on the Number of Variables for Graph Identification, Proceedings of 30th IEEE Symposium on Foundations of Computer Science (1989), 612–617.
A. Chandra and D. Harel, Computable Queries for Relational Data Bases, Journal of Computer and System Sciences 21 (1980), 156–178.
K. Compton, 0-1 Laws in Logic and Combinatorics, in: NATO Adv. Study Inst. on Algorithms and Order, I. Rival (Ed.), 1988, 353–383.
K. Compton, C. Henson and S. Shelah, Nonconvergence, undecidability and intractability in asymptotic problems, Annals of Pure and Applied Logic 36 (1987), 207–224.
P. Crescenzi and V. Kann, A compendium of NP optimization problems, preprint (1995).
A. Dawar, Feasible Computation through Model Theory, PhD thesis, University of Pennsylvania (1993).
R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, SIAM-AMS Proceedings 7 (1974), 43–73.
E. Grädel and K. Meer, Descriptive Complexity Theory over the Real Numbers, Proceedings of 27th ACM Sympposium on Theory of Computing (1995).
E. Grädel and M. Otto, Inductive Definability with Counting on Finite Structures, in: Selected Papers, 6th Workshop on Computer Science Logic CSL 92, San Miniato 1992, Lecture Notes in Computer Science Nr. 702, Springer (1993), 231–247.
J. Gross and T. Tucker, Topological Graph Theory, Wiley, New York (1987).
S. Grumbach and J. Su, Finitely representable databases, Proceedings of 13th ACM Symposium on Principles of Database Systems (1994).
Y. Gurevich, Toward logic tailord for computational complexity, in: M. M. Richter et al. (Eds), Computation and Proof Theory, Springer Lecture Notes in Mathematics Nr. 1104 (1984), 175–216.
Y. Gurevich, Logic and the Challenge of Computer Science, in: E. Börger (Ed), Trends in Theoretical Computer Science, Computer Science Press (1988), 1–57.
Y. Gurevich, Evolving Algebras 1993: Lipari Guide, in: E. Börger (Ed.), Specification and Validation Methods, Oxford University Press, to appear.
Y. Gurevich and S. Shelah, Fixed Point Extensions of First Order Logic, Annals of Pure and Applied Logic 32 (1986), 265–280.
T. Hirst and D. Harel, Completeness Results for Recursive Databases, Journal of Computer and System Sciences, to appear. (Also: 12th ACM Symp. on Principles of Database Systems (1993), 244–252.)
T. Hirst and D. Harel, More about Recursive Structures: Zero-One Laws and Expressibility vs. Complexity, unpublished (1995).
B. Hodgson and C. Kent, A Normal form for Arithmetical Representation of NP-sets, Journal of Computer and System Sciences 27 (1983), 378–388.
N. Immerman, Upper and lower bounds for first-order expressibility, Journal of Computer and Systems Sciences 25 (1982), 86–104.
N. Immerman, Relational Queries Computable in Polynomial Time, Information and Control 68 (1986), 86–104.
N. Immerman, Expressibility as a Complexity Measure: Results and Directions, Proc. of 2nd Conf. on Structure in Complexity Theory (1987), 194–202.
N. Immerman, Descriptive and Computational Complexity, in: J. Hartmanis (Ed.), Computational Complexity Theory, Proc. of AMS Symposia in Appl. Math. 38 (1989), 75–91.
N. Immerman and E. Lander, Describing Graphs: A First Order Approach to Graph Canonization, in: A. Selman (Ed), Complexity Theory Retrospective. (In Honor of Juris Hartmanis), Springer, New York 1990, 59–81.
J. Jones and Y. Matijasevich, Register machine proof of the theorem of exponential diophantine representation of enumerable sets, Journal of Symbolic Logic 49 (1984), 818–829.
F. Kabanza, J. Stevenne and P. Wolper, Handling Infinite Temporal Data, to appear in Journal of Computer and System Sciences. A preliminary version appeared in Proceedings of 9th ACM Syposium on Principles of Database Systems (1990).
P. Kanellakis, Elements of Relational Database Theory, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, vol. B, North Holland, Amsterdam 1990, pp. 1073–1156.
P. Kanellakis, G. Kuper and P. Revesz, Constraint Query Languages, Proceedings of 9th ACM Symposium on Principles of Database Systems (1990), 299–313.
C. Kent and B. Hodgson, An arithmetical characterization of NP, Theoretical Computer Science 12 (1982), 255–267.
J. Lynch, Almost sure theories, Annals of Mathematical Logic 18 (1980), 91–135.
Y. Matijasevich, Hilbert's Tenth Problem, MIT Press, Cambridge (1993).
M. Otto, Generalized Quantifiers for Simple Properties, Proceedings of IEEE Symposium on Logic in Computer Science (1994), 30–39.
M. Otto, The Expressive Power of Fixed-Point Logic with Counting, Journal of Symbolic Logic, to appear.
M. Otto, Habilitationsschrift, RWTH Aachen 1995.
C. Papadimitriou and M. Yannakakis, Optimization, approximization and complexity classes, Journal of Computer and System Sciences 43 (1991), 425–440.
B. Poizat, Deux ou trois choses que je sais de Ln, Journal of Symbolic Logic 47 (1982), 641–658.
S. Shelah, The very weak zero-one law for random graphs with order and random binary functions, preprint (1994).
J. Spencer, Nonconvergence in the theory of random orders, Order 7 (1991), 341–348.
J. Tyszkiewicz, private communication.
J. D. Ullman, Database and Knowledge-Base Systems, Vol. I and II, Computer Science Press (1989).
M. Vardi, Complexity of Relational Query Languages, Proc. of 14th Symposium on Theory of Computing (1982), 137–146.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grädel, E., Gurevich, Y. (1995). Metafinite model theory. In: Leivant, D. (eds) Logic and Computational Complexity. LCC 1994. Lecture Notes in Computer Science, vol 960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60178-3_92
Download citation
DOI: https://doi.org/10.1007/3-540-60178-3_92
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60178-4
Online ISBN: 978-3-540-44720-7
eBook Packages: Springer Book Archive