New results on quantifier elimination over real closed fields and applications to constraint databases

Journal of the ACM

Volumn 46, Issue 4, 1999, Pages 537-555

  Basu, Saugata ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT DATABASES; FIRSDT-ORDER EXPRESSIBILITY; REAL CLOSED FIELDS; UNIFORM QUANTIFIER ELIMINATION;

ALGORITHMS; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; POLYNOMIALS; PROBLEM SOLVING; QUERY LANGUAGES; SEMANTICS;

DATABASE SYSTEMS;

EID: 0001625774     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/320211.320240     Document Type: Article

References (33)

1. AGARWAL, P. K., AND MATOUSEK, J. 1994. On range searching with semi-algebraic sets. Disc. Computat. Geom. 11, 393-418.
2. BASU, S. 1997. Uniform quantifier elimination and constraint query processing. In Proceedings of the International Symposium on Symbolic and Algebraic Computation. ACM, New York, pp. 21-27.
3. BASU, S., POLLACK, R., AND ROY, M.-F. 1996. On the combinatorial and algebraic complexity of quantifier elimination. J. ACM 43, 6 (Nov.), 1002-1045.
4. BASU, S., POLLACK, R., AND ROY, M.-F. 1998. 1998. Complexity of computing semi-algebraic descriptions of the connected components of a semi-algebraic set. In Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISAAC '98) (Rostock, Germany, Aug. 13-15). ACM, New York, pp. 25-29.
5. BASU, S. 1998. On the combinatorial and topological complexity of a single cell. In Proceedings of the Symposium on the Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 606-616.
6. BENEDIKT, M., DONG, G., LIBKIN, L., AND WONG, L. 1998. Relational expressive power of constraint query languages. J. ACM 45 1 (Jan.), 1-34.
7. BENEDIKT, M., AND LIBKIN, L. 1996. On the structure of queries in constraint query languages. In Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 25-34.
8. BENEDIKT, M., AND LIBKIN, L. 1997. Languages for relational databases over interpreted structures. In Proceedings of the 16th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (Tucson, Az., May 12-14). ACM, New York, pp. 87-98.
9. BOCHNAK, J., COSTE, M., AND ROY, M.-F. 1987. Géométric algébrique réeile. Springer-Verlag, New York.
10. CHAZELLE, B. 1994. Computational geometry: A retrospective. In Proceedings of the 26th Annual ACM Symposium on Theory of Computing (Montreal, Que., Canada, May 23-25). ACM, New York, pp. 75-94.
11. COLLINS, G. E. 1975. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Lecture Notes in Computer Science, vol. 33. Springer-Verlag, New York, pp. 515-532.
12. COSTE, M., AND ROY, M.-F. 1988. Thom's lemma, the coding of real algebraic numbers and the topology of semi-algebraic sets. J. Symb. Comput. 5, 121-129.
13. EHRENFEUCHT, A. 1961. An application of games to the completeness problem for formalized theories. Fund. Math 49, 129-141.
14. FAGIN, R. 1993. Finite model theory - A personal perspective. Theoret. Comput. Sci. 116, 1, 3-31.
15. GAIFMAN, H. 1981. On local and non-local properties. In Proceedings of the Herbrand Symposium Logic Colloquium. North-Holland, Amsterdam, The Netherlands, pp. 105-135.
16. GRUMBACH, S., AND SU, J. 1997. Queries with arithmetical constraints. Theoret. Comput. Sci. 173, 1, 151-181.
17. GRUMBACH, S., AND SU, J. 1994. Finitely representable databases. In Proceedings of the 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (Minneapolis, Minn., May 24-26). ACM, New York, pp. 289-300.
18. GRUMBACH, S., AND SU, J. 1995. Dense-order constraint databases. In Proceedings of the 14th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (San Jose, Calif., May 22-25). ACM, New York, pp. 66-77.
19. GRIGOR'EV, D. 1988. The complexity of deciding Tarski algebra. J. Symb. Computat. 5, 65-108.
20. GUREVICH, Y. 1988. Logic and the challenge of computer science. In Current Trends in Theoretical Computer Science. Computer Science Press, Rockville, Md., pp. 1-57.
21. HALPERIN, D., AND SHARIR, M. 1994. New bounds for lower envelopes in three dimensions, with applications to visibility in terrains. Disc. Computat. Geom. 12, 313-326.
22. HALPERIN, D., AND SHARIR, M. 1995. Almost tight upper bounds for the single cell and zone problems in three dimensions. Disc. Computat. Geom. 14, 385-410.
23. HEINTZ, J., ROY, M. F., AND SOLERNO, P. 1990. Sur la complexité du principe de Tarski-Seidenberg. Bull. Soc. Math France 118, 101-126.
24. HEINTZ, J., ROY, M.-F., AND SOLERNO, P. 1994. Description of the connected components of a semialgebraic set in single exponential time. Disc. Computat. Geom. 11, 121-140.
25. KANELLAKIS, P., AND GLODIN, D. Q. 1994. Constraints programming and database query languages. In Proceedings of the 2nd Conference on Theoretical Aspects of Computer Software (TACS). Lecture Notes in Computer Science, vol. 789. Springer-Verlag, New York.
26. KANELLAKIS, P., KUPER, G., AND REVESZ, P. 1990. Constraint query languages. In Proceedings of the 9th Annual ACM Symposium on Principles of Database Systems (Nashville, Tenn., Apr. 2-4). ACM, New York, pp. 299-313.
27. RENEGAR, J. 1992. On the computational complexity and geometry of the first order theory of the reals. J. Symb. Comput. 13, 3, 255-352.
28. SEIDENBERG, A. 1954. A new decision method for elementary algebra. Ann. Math. 60, 365-374.
29. SHARIR, M. 1994. Almost tight upper bounds for lower envelopes in higher dimensions. Disc. Computat. Geom. 12, 327-345.
30. TARSKI, A. 1951. A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley, Calif.
31. ULLMAN, J. D. 1983. Principles of Database Systems. Computer Science Press, Rockville, Md.
32. WEISPFENNING, V. 1988. The complexity of linear problems in fields. J. Symb. Computat. 5, 3-27.
33. ZIEGLER, G. M. 1994. Lectures on Polytopes. Springer-Verlag, New York.