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Computational complexity and constraint logic programming languages

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Abstract

We give a complexity analysis of a variety of languages across the spectrum of the CLP scheme. By varying the logic and memory management, the role of the constraints and the role of the logic can be measured. The analysis clarifies the relation between linear/integer programming and constraint logic programming. We also determine how the power of constraints can easily lead to undecidable queries in Datalog languages with constraints. This work is motivated in large part by the problems of efficient implementation of CLP languages and the concomitant need for low level constraint languages.

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References

  1. J. Canny, Some algebraic and geometric computations in PSPACE,ACM Symp. on Theory of Computing (1988).

  2. A. Chandra, H. Lewis and J. Makowsky, Embedded implicational dependencies and their inference problem,ACM Symp. on Theory of Computing (1981) pp. 342–354.

  3. A. Chandra, D. Kozen and L. Stockmeyer, Alternation, J. ACM 28 (1981) 114–133.

    Google Scholar 

  4. A. Colmerauer, Opening the Prolog III universe: a new generation of Prolog promises some powerful capabilities, BYTE (Aug. 1987) 177–182.

  5. A.L. Christov and D.Y. Grigor'ev, Complexity of quantifier elimination in the theory of algebraically closed fields, J. Symbolic Comput. (1988).

  6. M. Davis, Y. Matiasevitch and J. Robinson,Proc. Symp. in Pure Mathematics: Mathematical Developments Arising From Hilbert Problems, vol. 28 (1976) pp. 323–378.

    Google Scholar 

  7. M. Dincbas, P. Van Hentenryck, H. Simonis, A. Aggoun, T. Graf and F. Berthier, The Constraint Logic Programming language CHIP,Proc. Int. Conf. on Fifth Generation Computing Systems (1988).

  8. P. Domich, R. Kannan and L. Trotter, Hermite normal form computation using modulo determinant arithmetic, Math. Oper. Res. 12 (1987) 50–59.

    Google Scholar 

  9. G. Gallo and B. Mishra, Efficient algorithms and bounds for Wu-Ritt characteristic sets, N.Y.U.-Courant Institute Technical Report No. 478 (1989).

  10. D. Ierardi, Quantifier elimination in the theory of an algebraically-closed field,ACM Symp. on Theory of Computing (1989).

  11. J. Jaffar and J.L. Lassez, Constraint Logic Programming, Monash University Technical Report (1986).

  12. J. Jaffar and J.L. Lassez, Constraint Logic Programming,Principles of Programming Languages (Munich, 1987).

  13. J. Jaffar and S. Michaylov, Methodology and implementation of a CLP system,Proc. 1987 Logic Programming Conf., Melbourne (MIT Press, 1987).

  14. N. Jones and W. Laaser, Complete problems for deterministic polynomial time, Theor. Comput. Sci. 3 (1977) 107–117.

    Google Scholar 

  15. P. Kanellakis, G. Kuper and P. Revesz, Constraint query languages,Principles of DataBase Systems (Nashville, 1990).

  16. J.-L. Lassez and K. McAloon, Applications of a canonical form for generalized linear constraints,Proc. 1988 Fifth Generation Computing Systems Conf., Tokyo (1988) pp. 703–710.

  17. J.-L. Lassez and K. McAloon, A canonical form for generalized linear constraints, to appear in J. Symbolic Comput.

  18. J. Lloyd,Foundations of Logic Programming (Springer, 1984).

  19. M.J. Maher, Logic semantics for a class of committed-choice programs,Proc. 1987 Logic Programming Conf., Melbourne (MIT Press, 1987) pp. 858–876.

  20. D. Maier and D.S. Warren,Computing with Logic (Addison-Wesley, 1988).

  21. V. Marek, A. Nerode and J. Remmel, A theory of non-monotonic rule systems,Logic in Computer Science '90, pp. 79–94.

  22. Y. Matiasevitch, Enumerable sets are diophantine, Sov. Math. Dokl. 11 (1980) 354–358.

    Google Scholar 

  23. K. McAloon and C. Tretkoff, 2LP: A logic programming and linear programming system, Brooklyn College Computer Science Technical Report No. 1989-21.

  24. M.S. Paterson and M.N. Wegman, Linear unification, J.CSS 16 (1978) 158–167.

    Google Scholar 

  25. J. Renegar, A faster PSPACE algorithm for deciding the Existential Theory of the Reals,IEEE Symp. on Foundations of Computer Science '88.

  26. K. Sakai, and A. Aiba, CAL: Theoretical background of Constraint Logic Programming and its applications, J. Symbolic Comput. 8 (1989) 589–604.

    Google Scholar 

  27. A. Schrijver,Theory of Linear and Integer Programming (Wiley, 1986).

  28. J. Schwartz, J. Hopcroft and M. Sharir,Planning, Geometry and Complexity of Robot Motion Planning (Albex, 1987).

  29. E. Shapiro, Alternation and the computational complexity of logic programs, J. Logic Progr. (1984) 19–33.

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Authors and Affiliations

  1. Brooklyn College, 11210, Brooklyn, NY

    Jim Cox, Ken McAloon & Carol Tretkoff

  2. CUNY Graduate Center, 10021, New York, NY, USA

    Jim Cox, Ken McAloon & Carol Tretkoff

Authors
  1. Jim Cox
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  2. Ken McAloon
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  3. Carol Tretkoff
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Additional information

Research partially supported by PSC-CUNY Grant 669287.

Research partially supported by NSF Grant IRI-8902511.

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Cox, J., McAloon, K. & Tretkoff, C. Computational complexity and constraint logic programming languages. Ann Math Artif Intell 5, 163–189 (1992). https://doi.org/10.1007/BF01543475

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