A fixed-point logic with symmetric choice

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2803, Issue , 2003, Pages 169-182

  Dawar, Anuj ^a   Richerby, David ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

POLYNOMIAL APPROXIMATION; RECONFIGURABLE HARDWARE; SEMANTICS; SET THEORY; TURING MACHINES;

EXPRESSIVE POWER; FIXED-POINT LOGIC; GRAPH ISOMORPHISM; GRAPH ISOMORPHISM PROBLEM; INDUCTIVE CONSTRUCTION; NONDETERMINISTIC CHOICE; PARAMETERIZED; POLYNOMIAL-TIME;

COMPUTER CIRCUITS;

EID: 29344475013     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-45220-1_16     Document Type: Article

References (20)

1. V. Arvind and S. Biswas. Expressibility of first order logic with a nondeterministic inductive operator. In Proceedings of 4th Annual Symposium on Theoretical Aspects of Computer Science, vol. 247 of Lecture Notes in Computer Science, pp. 323-335. Springer-Verlag, 1987.
2. A. Blass and Y. Gurevich. The logic of choice. Journal of Symbolic Logic, 65(3):1264-1310, 2000.
3. R.B. Boppana, J. Håstad and S. Zachos. Does co-NP have short interactive proofs? Information Processing Letters, 25(2):127-132, 1987.
4. J.-Y. Cai, M. Fürer and N. Immerman. An optimal lower bound on the number of variables for graph identification. Combinatorica, 12(4):389-410, 1992.
5. A. Dawar. Generalized quantifiers and logical reducibilities. Journal of Logic and Computation, 5(2):213-226, 1995.
6. A. Dawar and D.M. Richerby. Fixed-point logics with nondeterministic choice. Journal of Logic and Computation. To appear.
7. H.-D. Ebbinghaus. Extended logics: The general framework. In J. Barwise and S. Feferman, editors, Model-Theoretic Logics, Perspectives in Mathematical Logic, pp. 25-76. Springer-Verlag, 1985.
8. H.-D. Ebbinghaus and J. Flum. Finite Model Theory, 2nd edition. Springer-Verlag, 1999.
9. R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets. In R. Karp, editor, Complexity of Computation, vol. 7 of SIAM-AMS Proceedings, pp. 43-73. SIAM-AMS, 1974.
10. F. Gire and H.K. Hoang. An extension of fixpoint logic with a symmetry-based choice construct. Information and Computation, 144:40-65, 1998.
11. M. Grohe and J. Mariño. Definability and descriptive complexity on databases of bounded tree-width. In Proceedings of 7th International Conference on Database Theory, vol. 1540 of Lecture Notes in Computer Science, pp. 70-82. Springer-Verlag, 1999.
12. M. Grohe. Fixed-point logics on planar graphs. In Proceedings of 13th IEEE Annual Symposium on Logic in Computer Science, pp. 6-15. IEEE Computer Society, 1998.
13. M. Grohe. Isomorphism testing for embeddable graphs through definability. In Proceedings of 32nd ACM Symposium on Theory of Computing, pp. 63-72. ACM, 2000.
14. M. Gyssens, J. Van den Bussche and D. Van Gucht. Expressiveness of efficient semi-deterministic choice constructs. In Proceedings of 21st International Colloquium on Automata, Languages and Programming, vol. 820 of Lecture Notes in Computer Science, pp. 106-117. Springer-Verlag, 1994.
15. N. Immerman and E.S. Lander. Describing graphs: A first-order approach to graph canonization. In A. Selman, editor, Complexity Theory Retrospective, pp. 59-81. Springer-Verlag, 1990.
16. N. Immerman. Relational queries computable in polynomial time. Information and Control, 68(1-3):86-104, 1986.
17. M. Otto. Bounded Variable Logics and Counting - A Study in Finite Models, vol. 9 of Lecture Notes in Logic. Springer-Verlag, 1997.
18. U. Schöming. Graph isomorphism is in the low hierarchy. Journal of Computer and System Sciences, 37(3):312-323, 1988.
19. J. Torán. On the hardness of graph isomorphism. In Proceedings of 41st Annual Symposium on Foundations of Computer Science, pp. 180-186. IEEE Computer Society, 2000.
20. M. Y. Vardi. Complexity of relational query languages. In Proceedings of 14th ACM Symposium on Theory of Computing, pp. 137-146. ACM, 1982.