Skip to main content

The complexity of weak unification of bounded simple set terms

  • Active and Temporal Aspects 2
  • Conference paper
  • First Online:
  • 144 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1134))

Abstract

In this paper we consider the problem of weak unification of bounded simple set terms. Simple set terms are of the form {e 1, ..., e n}, where e i is a constant or a variable and are much used in deductive database systems such as \(\mathcal{L}\mathcal{D}\mathcal{L}\)and Coral. We consider a restricted form of unification, called “weak unification”, which is mainly used in the field of deductive databases where the database may contain both constants and variables and the program is “safe”. The main result of the paper is the detailed complexity analysis of the weak unification problem by providing a formula for determining the number of weak unifiers.

Work partially supported by a European Union grant under the EU-US project “DEUS EX MACHINA: non-determinism for deductive databases” and by a MURST project “Sistemi formali e strumenti per basi di dati evolute”.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abiteboul and S. Grumbach, COL: A logic-based language for complex objects, Proc. EDBT, pp. 271–293, 1988.

    Google Scholar 

  2. S. Abiteboul and P. Kanellekis, Object Identity as a Query language primitive, Proc. ACM SIGMOD Conf. on Management of Data, 1989.

    Google Scholar 

  3. P. Arenas-Sanchez, and A. Dovier, Minimal Set Unification, Proc. GULP-PRODE'95 Joint Conf. on Declarative Programming, 1995, pages 447–458.

    Google Scholar 

  4. N. Arni, S. Greco and D. Saccà, Matching of Bounded Set Terms in the Logic Language LDL++, Journal of Logic Programming (to appear).

    Google Scholar 

  5. C. Beeri, S. Naqvi, O. Shmueli and S. Tsur, Set Constructors in a Logic Database Language, Journal of Logic Programming, Vol. 10, No 3 & 4, Apr.May, 1991.

    Google Scholar 

  6. W. Buttner, Unification in the Data Structure Sets, Proc. 8th Int. Conf. on Automated Deduction, 1986, pages 470–488.

    Google Scholar 

  7. A. Dovier, E. G. Omodeo, E. Pontelli and G. F. Rossi, {log: A Logic Programming Language with Finite Sets, Proc. 8th Int. Conf. on Logic Progr., 1991.

    Google Scholar 

  8. F. Fages, Associative-Commutative Unification, 8th Int. Conf. on Automated Deduction, 1986, 416–430.

    Google Scholar 

  9. S. Greco, Optimal Unification of Bounded Simple Set Terms, Tech. Report, 1996.

    Google Scholar 

  10. S. Greco, C. Mateis, E. Spadafora, Unification of Bounded Simple Set Terms in Deductive Databases, Technical Report ISI-CNR, 1996.

    Google Scholar 

  11. N. Immerman, S. Patnaik and D. Stemple, The Expressiveness of a Family of Finite Set Languages, Proc. of the Tenth ACM Symposium on Principles of Database Systems, pages 37–52, 1991.

    Google Scholar 

  12. Jayaraman, B.: Implementation of Subset-Equational Programs, Journal of Logic Programming, Vol. 12, 299–324, April 1992.

    Article  Google Scholar 

  13. P. C. Kanellakis, G. M. Kuper, and P. Z. Revez: Constraint query languages, Proc. Int. Symp. on Princ. of Database Systems, 1990.

    Google Scholar 

  14. Kapur, D., Narendran, P.: NP-completeness of the Set Unification and Matching problems, Proc. 8th Int. Conf. on Automated Deduction, 489–495, 1986.

    Google Scholar 

  15. Kapur, D., Narendran, P.: Double-Exponential Complexity of Computing a Complete Set of AC-Unifiers. Proc. 8th Conf. on Logic in Computer Sc., 11–21, 1992.

    Google Scholar 

  16. Kifer, M., Lausen, G.: F-Logic: A Higher-Order Language for Reasoning About Objects, Inheritance and Scheme, Proc. ACM SIGMOD Conference, 134–146, 1989.

    Google Scholar 

  17. Knight, K.: Unification: A Multidisciplinary Survey, ACM Comp. Surveys, Vol. 21, No. 1, 1989, 93–124.

    Article  Google Scholar 

  18. Kuper, G. M.: Logic Programming with Sets, J. of Computer and System Science, No. 41, 1990, 44–64.

    Article  Google Scholar 

  19. C. Lincoln and J. Christian, Adventures in Associative-Commutative Unification, Proc. 9th International Conference on Automated Deduction, 1988, pages. 358–367.

    Google Scholar 

  20. M Livesey and J.H. Siekmann, Unification of A+C-Terms (Bags) and A+C+I-Terms (Sets), Tech. Report, 5/67, Facultat fur Informatik, Univ. Karlruhe, 1976.

    Google Scholar 

  21. S. Naqvi and S. Tsur, A logical Language for Data and Knowledge Bases, Comp. Science Press, 1989.

    Google Scholar 

  22. R. Ramakrisnhan, D. Srivastava, and S. Sudanshan. CORAL — Control, Relations and Logic. In Proc. of 18th VLDB Conference, 1992.

    Google Scholar 

  23. O. Shmueli, S. Tsur and C. Zaniolo, Compilation of Set Terms in the Logic Data Language (LDL), Journal of Logic Programming, Vol. 12, No 1 & 2, Jan.Feb., 1992, pages 89–119.

    Article  MathSciNet  Google Scholar 

  24. J. Siekmann, Unification Theory, Journal of Symbolic Computation, No. 7, 1989, pages 207–274.

    Google Scholar 

  25. M.E. Stickel, A Unification Algorithm for Associative-Commutative Functions, Journal of ACM Vol. 28, No. 3, 1981, pages. 423–434.

    Article  Google Scholar 

  26. F. Stolzenburg, An Algorithm for general Set Unification and its Complexity, Proc. ICLP Workshop on Sets in Logic Programming 1994.

    Google Scholar 

  27. S. Tsur and C. Zaniolo, LDL: A Logic Based Data Language Proc. 12th Conference on Very Large Data Bases, 1986.

    Google Scholar 

  28. J.K. Ullman, Principles of Database and Knowledge-Base Systems, Vol. 1, Computer Science Press, Rockville, Md., 1988.

    Google Scholar 

  29. R. M. Verma and I. V. Ramakrishnan, Tight Complexity Bound for Term Matching Problems, Information and Computation, No. 101, pages 33–69, 1992.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Roland R. Wagner Helmut Thoma

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Greco, S., Mateis, C., Spadafora, E. (1996). The complexity of weak unification of bounded simple set terms. In: Wagner, R.R., Thoma, H. (eds) Database and Expert Systems Applications. DEXA 1996. Lecture Notes in Computer Science, vol 1134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034683

Download citation

  • DOI: https://doi.org/10.1007/BFb0034683

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61656-6

  • Online ISBN: 978-3-540-70651-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics