Technique for proving decidability of containment and equivalence of linear constraint queries

Journal of Computer and System Sciences

Volumn 59, Issue 1, 1999, Pages 1-28

  Ibarra, Oscar H ^a   Su, Jianwen ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; EQUIVALENCE CLASSES; LINGUISTICS; NUMBER THEORY; POLYNOMIALS; THEOREM PROVING;

CONTAINMENT; EQUIVALENCE; LINEAR CONSTRAINT QUERIES;

QUERY LANGUAGES;

EID: 0033169437     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1999.1624     Document Type: Article

References (50)

1. Abiteboul S., Hull R., Vianu V. Foundations of Databases. 1995;Addison-Wesley, Reading.
2. Aho A. V., Sagiv Y., Ullman J. D. Efficient optimization of a class of relational expressions. ACM Trans. Database Systems. 4:1979;435-454.
3. Aho A. V., Sagiv Y., Ullman J. D. Equivalence among relational expressions. SIAM J. Comput. 8:1979;218-246.
4. Baker B., Book R. Reversal-bounded multipushdown machines. J. Comput. System Sci. 8:1974;315-332.
5. Benedikt M., Dong G., Libkin L., Wong L. Relational expressive power of constraint query languages. J. Assoc. Comput. Mach. 45:1998;1-34.
6. M. Benedikt, and, L. Libkin, On the structure of queries in constraint query languages, in, Proc. IEEE Symposium on Logic In Computer Science, 1996.
7. Chandra A. K., Harel D. Computable queries for relational data bases. J. Comput System Sci. 21:1980;156-178.
8. Chen P. P.-S. The entity-relationship model - toward a unified view of data. ACM Trans. Database Systems. 1:1976;9-36.
9. Chang C. C., Keisler H. J. Model Theory. Studies in Logic. 73:1973;North-Holland, Amsterdam.
10. Chandra A. K., Merlin P. M. Optimal implementation of conjunctive queries in relational data bases. Proc. ACM SIGACT Symp. on the Theory of Computing. 1977;. p. 77-90.
11. Codd E. F. A relational model of data for large shared data banks. Comm. Assoc. Comput. Mach. 13:1970;377-387.
12. Chaudhuri S., Vardi M. Y. Optimization of real conjunctive queries. Proc. ACM Symp. on Principles of Database Systems. 1993;. p. 59-70.
13. Dong G., Su J. Conjunctive query containment with respect to views and constraints. Inform. Process. Lett. 57:1996;95-102.
14. Ehrenfeucht A. An application of games to the completeness problem for formalized theories. Fund. Math. 49:1961.
15. Enderton H. B. A Mathematical Introduction to Logic. 1972;Academic Press, New York.
16. Fagin R. Finite model theory - A personal perspective. Theoret. Comput. Sci. 116:1993;3-31.
17. Fischer M. J., Rabin M. O. Super-exponential complexity of Presburger arithmetic. SIAM-AMS Proc. 7:1974;27-41.
18. Ferrante J., Rackoff C. W. A decision procedure for the first order theory of real addition with order. SIAM J. Comput. 4:1975;69-76.
19. Fraïssé R. Sur les classifications des systèmes de relations. Publ. Sci. Univ. Alger. I:1954;1.
20. Fagin R., Stockmeyer L. J., Vardi M. Y. On monadic NP vs. monadic co-NP. Inform. and Comput. 120:1995;78-92.
21. Fürer M. The complexity of Presburger arithmetic with bounded quantifier alternation depth. Theoret. Comput. Sci. 18:1982;105-111.
22. Gaifman H. On local and non-local properties. Stern J. Proc. Herbrand Symposium Logic Colloquium. 1981;105-135 North Holland, Amsterdam.
23. Gurari E. M., Ibarra O. H. An NP-complete number-theoretic problem. Assoc. Comput. Mach. 26:1979;567-581.
24. Gurari E. M., Ibarra O. H. The complexity of decision problems for finite-turn multicounter machines. J. Comput. System Sci. 22:1981;220-229.
25. Gurari E. M., Ibarra O. H. Two-way counter machines and diophantine equations. J. Assoc. Comput. Mach. 29:1982;863-873.
26. Grumbach S., Su J. Dnese order constraint databases. Proc. ACM Symp. on Principles of Database Systems. 1995.
27. Grumbach S., Su J. Finitely representable databases. J. Comput. System Sci. 55:1997;273-298.
28. Grumbach S., Su J. Queries with arithmetical constraints. Theoret. Comput. Sci. 173:1997;151-181.
29. Hanf W. Model-theoretic methods in the study of elementary logic. Addison J., Henkin L., Tarski A. The Theory of Models. 1965;132-145 North Holland, Amsterdam.
30. Hammer M., McLeod D. Database description with SDM: A semantic database model. ACM Trans. Database Systems. 6:1981;351-386.
31. Ibarra O. H. Reversal-bounded multicounter machines and their decision problems. J. Assoc. Comput. Mach. 25:1978;116-133.
32. Ibarra O. H., Jiang T., Tran N., Wang H. New decidability results concerning two-way counter machines. SIAM J. Comput. 24:1995;123-137.
33. Kanellakis P. C., Goldin D. Q. Constraint programming and database query languages. Proc. 2nd Conf. Theoret. Aspects of Comput. Software (TACS). Lecture Notes in Computer Science. 789:1994;Springer-Verlag, New York.
34. Kanellakis P., Kuper G., Revesz P. Constraint query languages. J. Comput. System Sci. 51:1995;26-52.
35. Klug A. On conjunctive queries containing inequalities. J. Assoc. Comput. Mach. 35:1988;146-160.
36. Kuper G. M. Aggregation in constraint databases. Proc. Workshop on the Principles and Practice of Constraint Programming. 1993;. p. 176-183.
37. Libkin L., Wong L. Query languages for bags and aggregate functions. J. Comput. System Sci. 55:1997;241-272.
38. Minsky M. Recursive unsolvability of Post's problem of Tag and other topics in the theory of Turing machines. Ann. of Math. 74:1961;437-455.
39. M. Presburger, Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt, in C. R. Premier Congrès Math. Pays Slaves, Warsaw, 1929, pp. 92-101.
40. Paredaens J., Van den Bussche J., Van Gucht D. Towards a theory of spatial database queries. Proc. 13th ACM Symp. on Principles of Database Systems. 1994;. p. 279-88.
41. Paredaens J., Van den Busssche J., Van Gucht D. First-order queries on finite structures over the reals. SIAM J. Comput. 27:1998;1747-1763.
42. Revesz P. Z. A closed form for datalog queries with integer (gap)-order constraints. Theoret. Comput. Sci. 116:1993;117-149.
43. Reddy C. R., Loveland D. W. Presburger arithmetic with bounded quantifier alternation. Proc. ACM SIGADT Symp. on the Theory of Computing. 1978;. p. 320-325.
44. Stolboushkin A. P., Taitslin M. A. Linear vs. order constrained queries over rational databases. Proc. ACM Symp. on Principles of Database Systems. 1996.
45. Tarski A. A Decision Method for Elementary Algebra and Geometry. 1951;Univ. of California Press, Berkeley.
46. Ttrakhtenbrot B. A. The impossibility of an algorithm for the decision problem for finite models. Dokl. Akad. Nauk SSSR. 70:1950;569-572.
47. J. D. Ullman, Database and Knowledge-Base Systems, Vol, 1, Computer Science Press, New York, 1988.
48. Ullman J. U. Information integration using logical views. Proc. Int. Conf. Database Theory. 1997;. p. 19-40.
49. van der Meyden R. The complexity of querying indefinite data about linearly ordered domains. J. Comput. System Sci. 54:1997;113-135.
50. Valiant L., Patterson M. Deterministic one-counter automata. J. Comput. System Sci. 10:1975;340-350.