Finite model theory on tame classes of structures

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

Volumn 4708 LNCS, Issue , 2007, Pages 2-12

  Dawar, Anuj ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FORMAL LOGIC; MATHEMATICAL MODELS;

FINITE MODEL THEORY; FINITE STRUCTURES; TAME CLASSES;

FINITE DIFFERENCE METHOD;

EID: 38049021595     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-74456-6_2     Document Type: Conference Paper

References (42)

1. Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)
2. Ajtai, M., Gurevich, Y.: Datalog vs first-order logic. J. of Computer and System Sciences 49, 562-588 (1994)
3. Atserias, A., Dawar, A., Grohe, M.: Preservation under extensions on well-behaved finite structures. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1437-1449. Springer, Heidelberg (2005)
4. Atserias, A., Dawar, A., Kolaitis, P.G.: On preservation under homomorphisms and unions of conjunctive queries. Journal of the ACM 53, 208-237 (2006)
5. Babai, L., Luks, E.M.: Canonical labeling of graphs. In: Proc. of the 15th ACM Symp. on the Theory of Computing, pp. 171-183. ACM Press, New York (1983)
6. Benedikt, M., Segoufin, L.: Towards a characterization of order-invariant queries over tame structures. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 276-291. Springer, Heidelberg (2005)
7. Borger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, Heidelberg (1997)
8. Cai, J-Y., Fürer, M., Immerman, N.: An optimal lower bound on the number of variables for graph identification. Combinatorica 12(4), 389-410 (1992)
9. Courcelle, B.: The monadic second-order logic of graphs ii: Infinite graphs of bounded width. Theory of Computing Systems 21, 187-221 (1989)
10. Courcelle, B.: Graph rewriting: An algebraic and logic approach. In: van Leeuwan, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Sematics (B), vol. B, pp. 193-242. Elsevier, Amsterdam (1990)
11. Dawar, A., Grohe, M., Kreutzer, S.: Locally excluding a minor. In: Proc. 22nd IEEE Symp. on Logic in Computer Science (2007)
12. Dawar, A., Grohe, M., Kreutzer, S., Schweikardt, N.: Model theory makes formulas large. In: ICALP'07: Proc. 34th International Colloquium on Automata, Languages and Programming. LNCS, Springer, Heidelberg (2007)
13. Dawar, A., Kreutzer, S., Grohe, M., Schweikardt, N.: Approximation schemes for first-order definable optimisation problems. In: Proc. 21st IEEE Symp. on Logic in Computer Science, pp. 411-420 (2006)
14. Dawar, A., Malod, G.: forthcoming
15. Dawar, A., Richerby, D.: The power of counting logics on restricted classes of finite structures. In: CSL 2007: Computer Science Logic. LNCS, Springer, Heidelberg (2007)
16. Diestel, R.: Graph Theory, 3rd edn. Springer, Heidelberg (2005)
17. Ebbinghaus, H-D., Flum, J.: Finite Model Theory. 2nd edn., Springer, Heidelberg (1999)
18. Eppstein, D.: Diameter and treewidth in minor-closed graph families. Algorithmica 27, 275-291 (2000)
19. Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R.M. (ed.) Complexity of Computation, SIAM-AMS Proceedings, vol. 7, pp. 43-73 (1974)
20. Flum, J., Grohe, M.: Fixed-parameter tractability, definability, and model checking. SIAM Journal on Computing 31, 113-145 (2001)
21. Frick, M., Grohe, M.: Deciding first-order properties of locally tree-decomposable structures. Journal of the ACM 48, 1184-1206 (2001)
22. Gaifman, H.: On local and non-local properties. In: Stern, J. (ed.) Proceedings of the Herbrand Symposium Logic Colloquium '81, pp. 105-135. North-Holland, Amsterdam (1982)
23. Grädel, E., Kolaitis, P.G., Libkin, L., Marx, M., Spencer, J., Vardi, M.Y., Venema, Y., Weinstein, S.: Finite Model Theory and Its Applications. Springer, Heidelberg (2007)
24. Grohe, M.: Fixed-point logics on planar graphs. In: Proc. 13th IEEE Annual Symp. Logic in Computer Science, pp. 6-15 (1998)
25. Grohe, M.: Isomorphism testing for embeddable graphs through definability. In: Proc. 32nd ACM Symp.Theory of Computing, pp. 63-72 (2000)
26. Grohe, M., Mariño, J.: Definability and descriptive complexity on databases of bounded tree-width. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, Springer, Heidelberg (1998)
27. Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)
28. Immerman, N.: Relational queries computable in polynomial time. Information and Control 68, 86-104 (1986)
29. Immerman, N.: Descriptive Complexity. Springer, Heidelberg (1999)
30. Immerman, N., Lander, E.S.: Describing graphs: A first-order approach to graph canonization. In: Selman, A. (ed.) Complexity Theory Retrospective, Springer, Heidelberg (1990)
31. Kolatis, P.G.: A tutorial on finite model theory. In: Proceedings of the Eighth Annual IEEE Symp. on Logic in Computer Science, LICS 1993, pp. 122-122 (1993)
32. Kreidler, M., Seese, D.: Monadic NP and graph minors. In: Gottlob, G., Grandjean, E., Seyr, K. (eds.) Computer Science Logic. LNCS, vol. 1584, pp. 126-141. Springer, Heidelberg (1999)
33. Libkin, L.: Elements of Finite Model Theory. Springer, Heidelberg (2004)
34. Lindell, S.: An analysis of fixed-point queries on binary trees. Theoretical Computer Science 85(1), 75-95 (1991)
35. Livchak, A.: The relational model for process control. Automated Documentation and Mathematical Linguistics 4, 27-29 (1983)
36. Luks, E.M.: Isomorphism of graphs of bounded valence can be tested in polynomial time. Journal of Computer and System Sciences 25, 42-65 (1982)
37. Mohar, B., Thomassen, C.: Graphs on Surfaces. Johns Hopkins University Press (2001)
38. Rossman, B.: Existential positive types and preservation under homomorphisisms. In: 20th IEEE Symposium on Logic in Computer Science, pp. 467-476 (2005)
39. Seese, D.: Linear time computable problems and first-order descriptions. Math. Struct, in Comp. Science 6, 505-526 (1996)
40. Nešetřil, J., de Mendez, P.O.: The grad of a graph and classes with bounded expansion. International Colloquium on Graph Theory, 101-106 (2005)
41. Tait, W.W.: A counterexample to a conjecture of Scott and Suppes. Journal of Symbolic Logic 24, 15-16 (1959)
42. Vardi, M.Y.: The complexity of relational query languages. In: Proc. of the 14th ACM Symp. on the Theory of Computing, pp. 137-146 (1982)