The expressive power of fixed-point logic with counting

Journal of Symbolic Logic

Volumn 61, Issue 1, 1996, Pages 147-176

  Otto, Martin ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030545743     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2307/2275602     Document Type: Article

References (27)

1. S. ABITEBOUL, M. Y. VARDI, and V. VIANU, Computing with infinitary logic, 4th international conference on database theory, ICDT '92, Lecture Notes in Computer Science 646, Springer-Verlag, 1992, pp. 113-123.
2. _, Fixpoint logics, relational machines, and computational complexity, Proceedings of the 7th IEEE conference on structure in complexity theory, 1992.
3. S. ABITEBOUL and V. VIANU, Fixpoint extensions of first-order logic and datalog-like languages, Proceedings of the 4th IEEE symposium on logic in computer science, 1989, pp. 71-79.
4. _, Datalog extensions for database queries and updates, Journal of Computer and Systems Science, vol. 43 (1991), pp. 62-124.
5. _, Generic computation and its complexity, Proceedings of the 23rd ACM symposium on theory of computing, 1991, pp. 209-219.
6. J. CAI, M. FÜRER, and N. IMMERMAN, An optimal lower bound on the number of variables for graph identification, Combinatoria, vol. 12 (1992), pp. 389-410; a prelimineary version appeared in Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, 1989, pp. 612-617.
7. J. CAI, M. FÜRER, and N. IMMERMAN, An optimal lower bound on the number of variables for graph identification, Combinatoria, vol. 12 (1992), pp. 389-410; a prelimineary version appeared in Proceedings of the 30th IEEE Symposium on Foundations of Computer Science, 1989, pp. 612-617.
8. A. DAWAR, S. LINDELL, and S. WEINSTEIN, Infinitary logic and inductive definability over finite structures, Information and Computation, vol. 119 (1995), pp. 160-175.
9. H.-D. EBBINGHAUS, Extended logics: The general framework, Model-theoretic logics (J. Barwise and S. Feferman, editors), Springer-Verlag, 1985, pp. 25-76.
10. E. GRÄDEL and M. OTTO, Inductive definability with counting on finite structures, Computer science logic, selected papers from CSL '92, Lecture Notes in Computer Science 702 (E. Börger et al., editors), Springer-Verlag, 1993, pp. 231-247.
11. M. GROHE, Diplomarbeit, Universität Freiburg, 1992.
12. S. GRUMBACH and C. TOLLU, Query languages with counters, Proceedings of the international conference on database theory, Lecture Notes in Computer Science 646 (J. Biskup and R. Hull, editors), Springer-Verlag, 1992, pp. 124-139.
13. Y. GUREVICH, Algebras of feasible functions, Proceedings of the 24th IEEE symposium on foundations of computer science, 1983, pp. 210-214.
14. _, Towards logic tailored for computational complexity, Computation and proof theory, Lecture Notes in Mathematics 1104 (M. M. Richter et al., editors), Springer-Verlag, 1984, pp. 175-216.
15. Y. GUREVICH and S. SHELAH, Fixed point extensions of first order logic, Annals of Pure and Applied Logic, vol. 32 (1986), pp. 265-280.
16. H. HÄRTIG, Über einen Quantifikator mit zwei Wirkungsbereichen, Colloqium on the foundations of mathematics, mathematical machines and their application (L. Kalmar, editor), 1965, pp. 31-36.
17. N. IMMERMAN, Upper and lower bounds for first-order expressibility, Journal of Computer and System Sciences, vol. 25 (1982), pp. 76-98.
18. _, Relational queries computable in polynomial time, Information and Control, vol. 68 (1986), pp. 86-104.
19. _, Expressibility as a complexity measure: Results and directions, Proceedings of the 2nd conference on structure in complexity theory, 1987, pp. 194-202.
20. _, Descriptive and computational complexity, Computational complexity theory, proceedings of the AMS symposium in applied mathematics (J. Hartmanis, editor), vol. 38, 1989, pp. 75-91.
21. N. IMMERMAN and E. LANDER, Describing graphs: A first order approach to graph canonization, Complexity theory retrospective (A. Selman, editor), Springer-Verlag, 1990, pp. 59-81.
22. PH. KOLAITIS and J. A. VÄÄNÄNEN, Generalized quantifiers and pebble games on finite structures, Proceedings of the 7th IEEE symposium on logic in computer science, 1992, pp. 348-359.
23. PH. KOLAITIS and M. VARDI, Infinitary logics and 0-1-laws, Information and Computation, vol. 98 (1992), pp. 258-294.
24. M. OTTO, Generalized quantifiers for simple properties, Proceedings of the 9th IEEE symposium on logic in computer science, 1994.
25. N. RESCHER, Plurality quantification, this JOURNAL, vol. 27 (1962), pp. 373-374.
26. M. VARDI, Complexity of relational query languages, Proceedings of the 14th ACM symposium on theory of computing, 1982, pp. 137-146.
27. I. WEGENER, The complexity of Boolean functions, Teubner, 1987.