Finitely Representable Databases

Journal of Computer and System Sciences

Volumn 55, Issue 2, 1997, Pages 273-298

  Grumbach, Stéphane ^a   Su, Jianwen ^b  

^a INRIA   (France)

^b University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; FORMAL LOGIC; GAME THEORY; MATHEMATICAL MODELS; POLYNOMIALS; QUERY LANGUAGES; THEOREM PROVING; TOPOLOGY;

EHRENFEUCHT FRAISSE GAMES; FINITELY REPRESENTABLE DATABASES;

RELATIONAL DATABASE SYSTEMS;

EID: 0031245267     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1997.1524     Document Type: Article

References (59)

1. F. Afrati, S. Cosmadakis, S. Grumbach, and G. Kuper, Expressiveness of linear vs. polynomial constraints in database query languages, in "Proceedings, Workshop on the Principles and Practice of Constraint Programming, 1994."
2. S. Abiteboul, R. Hull, and V. Vianu, "Foundations of Databases," Addison-Wesley, Reading, MA, 1995.
3. 1 formulae on finite structures, Ann. Pure Appl. Logic 24 (1983), 1-48.
4. S. Abiteboul and V. Vianu, Datalog extensions for database queries and updates, J. Comput. System Sci. 43, No. 1 (1991), 62-124.
5. M. Benedikt, G. Dong, L. Libkin, and L. Wong, Relational expressive power of constraint query languages, in "Proceedings, ACM Symposium on Principles of Database Systems, 1996."
6. M. Ben-Or, D. Kozen, and J. Reif, The complexity of elementary algebra and geometry, J. Comput. System Sci. 32, No. 2 (1986), 251-264.
7. M. Benedikt and L. Libkin, On the structure of queries in constraint query languages, in "Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, 1996."
8. J. Chomicki, D. Q. Goldin, and G. M. Kuper, Variable independence and aggregation closure, in "Proceedings, ACM Symposium on Principles of Database Systems, 1996."
9. A. K. Chandra and D. Harel, Computable queries for relational data bases, J. Comput. System Sci. 2, No. 2 (1980), 156-78.
10. A. K. Chandra and D. Harel, Structure and complexity of relational queries, J. Comput. System Sci. 25, No. 1 (1982), 99-128.
11. C. C. Chang and H. J. Keisler, "Model Theory," Studies in Logic, Vol. 73, North-Holland, Amsterdam, 1973.
12. E. F. Codd, A relational model of data for large shared data banks, Comm. ACM 13, No. 6 (1970), 377-387.
13. G. E. Collins, Quantifier elimination for real closed fields by cylindric decompositions, in "Proceedings, 2nd GI Conference Automata Theory and Formal Languages," Lecture Notes in Computer Science, Vol. 35, pp. 134-183, Springer-Verlag, New York/Berlin, 1975.
14. K. J. Compton, 0-1 laws in logic and combinatorics, in "NATO Adv. Study Inst. on Algorithms and Order" (I. Rival, Ed.), pp. 353-383, D. Reidel, 1988.
15. L. Van den Dries, A. Macintyre, and D. Marker, The elementary theory of restricted analytic fields with exponentiation, Ann. of Math. (1994).
16. L. Van den Dries, Remarks on Tarski's problem concerning (r, +, x, exp), in "Logic Colloquium" North-Holland/ Elsevier, New York, 1982.
17. H. D. Ebbinghaus, J. Flum, and W. Thomas, "Mathematical Logic," Springer-Verlag, New York/Berlin, 1984.
18. A. Ehrenfeucht, An application of games to the completeness problem for formalized theories, Fund. Math. 49 (1961).
19. H. B. Enderton, "A Mathematical Introduction to Logic," Academic Press, 1972.
20. R. Fagin, Probabilities on finite models, J. Symb. Logic 41, No. 1 (1976), 50-58.
21. R. Fagin, Finite model theory - a personal perspective, Theoretical Computer Science 116, No. 1 (1993), 3-31.
22. R. Fraïssé, Sur les classifications des systèmes de relations, Publ. Sci. Univ Alger I (1954), 1.
23. M. Furst, J. B. Saxe, and M. Sipser, Parity, circuits, and the polynomial-time hierarchy, Math. Systems Theory 17 (1984), 13-27.
24. H. Gaifman, On local and non local properties, in "Proceedings, Herbrand Symposium Logic Colloquium" (J. Stern, Ed.), pp. 105-135, North-Holland, 1981.
25. E. Grädel and Y. Gurevich, Metafinite model theory, in "Logic and Computational Complexity" (D. Leivant, Ed.), Lecture Notes in Computer Science, Vol. 960, Springer-Verlag, 1994.
26. S. Grumbach and J. Su, Finitely representable databases (extended abstract), in "Proceedings, ACM Symposium on Principles of Database Systems, 1994."
27. S. Grumbach and J. Su, Dense order constraint databases, in "Proceedings, 14th ACM Symposium on Principles of Database Systems, San Jose, May 1995."
28. S. Grumbach and J. Su, Queries with arithmetical constraints, Theoretical Computer Science (1996), to appear. An extended abstract appeared in "Proceedings, International Conference on Principles and Practice of Constraint Programming (CP95)" under the title "First-order Definability over Constraint Databases."
29. S. Grumbach and J. Su, Towards practical constraint databases, in "Proceedings, ACM Symposium on Principles of Database Systems, 1996."
30. S. Grumbach, J. Su, and C. Tollu, Linear constraint query languages: Expressive power and complexity, in "Logic and Computational Complexity: International Workshop LCC '94," Springer-Verlag, New York/Berlin, 1994.
31. T. Hirst and D. Harel, Completeness results of recursive data bases, in "Proceedings, 12th ACM Symposium on Principles of Database Systems, 1993," pp. 244-252.
32. T. Hirst and D. Harel, Recursive model theory, draft, 1994.
33. R. Hull and J. Su, On the expressive power of database queries with intermediate types, J. Comput. System Sci. 43, No. 1 (1991), 219-267.
34. R. Hull and J. Su, Algebraic and calculus query languages for recursively typed complex objects, J. Comput. System Sci. 47, No. 1 (1993), 121-56.
35. R. Hull and J. Su, Domain independence and the relational calculus, Acta Informatica 31, No. 6 (1994), 513-524.
36. R. Hull, Relative information capacity of simple relational schemata, SIAM J. Comput. 15, No. 3 (1986), 856-886.
37. N. Immerman, Relational queries computable in polynomial time, Inform. Control 68 (1986), 86-104.
38. N. Immerman, Languages that capture complexity classes, SIAM J. Comput. 16, No. 4 (1987), 760-778.
39. P. C. Kanellakis and D. Q. Goldin, Constraint programming and database query languages, in "Proceedings, 2nd Conference on Theoretical Aspects of Computer Software (TACS)," Vol. 789, Lecture Notes in Computer Science, Springer-Verlag, 1994.
40. P. Kanellakis, G. Kuper, and P. Revesz, Constraint query languages, J. Comput. System Sci. 51, No. 1 (1995), 26-52. (An extended abstract appeared in Proceedings, PODS '90).
41. B. Kuijpers, J. Paredaens, and J. Van den Bussche, Lossless representation of topological spatial data, in "Advances in Spatial Databases, 4th Int. Symp., SSD '95" (M. J. Egenhofer and J. R. Herring, Eds.), pp. 1-13, Springer, 1995.
42. P. Kanellakis, S. Ramaswamy, D. Vengroff, and J. Vitter, Indexing for data models with constraints and classes, in "Proceedings, ACM Symposium on Principles of Database Systems," pp. 233-243, 1993.
43. G. M. Kuper, On the expressive power of the relational calculus with arithmetic constraints, in "Proceedings, International Conference on Database Theory," pp. 202-211, 1990.
44. G. M. Kuper, Aggregation in constraint databases, in "Proceedings, Workshop on the Principles and Practice of Constraint Programming, April 1993," pp. 176-183.
45. G. M. Kuper, personal communications, 1993.
46. C. H. Papadimitriou, D. Suciu, and V. Vianu, Topological queries in spatial databases, in "Proceedings, ACM Symposium on Principles of Database Systems, 1996."
47. J. Paredaens, J. Van den Bussche, and D. Van Gucht, Towards a theory of spatial database queries, in "Proceedings, 13th ACM Symposium on Principles of Database Systems 1994," pp. 279-88.
48. J. Paredaens, J. Van den Bussche, and D. Van Gucht, First-order queries on finite structures over the reals, in "Proceedings, IEEE Symposium on Logic in Computer Science, 1995."
49. J. Renegar, On the computational complexity and geometry of the first-order theory of the reals, Journal of Symbolic Computation 13 (1992), 255-352.
50. P. Z. Revesz, A closed form for datalog queries with integer order, in "Proceedings, International Conference on Data-base Theory 1990," pp. 187-201.
51. A. P. Stolboushkin and M. A. Taitslin, Linear vs. order constrained queries over rational databases, in "Proceedings, ACM Symposium on Principles of Database Systems, 1996."
52. A. Tarski, "A Decision Method for Elementary Algebra and Geometry," University of California Press, Berkeley, CA, 1951.
53. B. A. Trakhtenbrot, The impossibility of an algorithm for the decision problem for finite models, Doklady Akademii Nauk SSR 70 (1950), 569-572.
54. J. D. Ullman, "Principles of Database Systems (2nd edition)," Computer Science Press, Potomac, Maryland, 1982.
55. M. Vardi, Relational queries computable in polynomial time, in "Proceedings, 14th ACM Symposium on Theory of Computing, 1982," pp. 137-146.
56. R. L. Vaught, Sentences true in all constructive models, J. Symb. Logic 25, No. 1 (1960), 39-53.
57. L. Vandeurzen, M. Gyssens, and D. Van Gucht, On the desirability and limitations of linear spatial database models, in "Advances in Spatial Databases, 4th International Symposium, SSD '95" pp. 14-28, Springer, 1995.
58. V. Vianu, personal communications, 1993.
59. F. F. Yao, Computational geometry, in "Handbook of Theoretical Computer Science" (J. van Leeuwen, Ed.), Vol. A, Chap. 7, pp. 343-389, North-Holland, 1990.