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Recurrence with affine level mappings is P-time decidable for CLP

  • FRED MESNARD (a1) and ALEXANDER SEREBRENIK (a2)
Abstract
Abstract

In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.

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Afrati F. N., Cosmadakis S. S. and Foustoucos E. 2005. Datalog programs and their persistency numbers. ACM Transactions on Computational Logic (TOCL) 6 (3), 481518.
Basu S., Pollack R. and Roy M.-F. 1996. On the combinatorial and algebraic complexity of quantifier elimination. Journal of the ACM 43 (6), 10021045.
Bezem M. 1993. Strong termination of logic programs. Journal of Logic Programming 15 (1&2), 7997.
Collins G. E. 1975. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Second GI Conference on Automata Theory and Formal Languages. Lecture Notes in Computer Science, Vol. 33. Springer, 134–183.
Cousot P. 2005. Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming. In Verification, Model Checking, and Abstract Interpretation, 6th International Conference, VMCAI, Paris, France, January 17–19, 2005, Proceedings, Cousot R., Ed. Lecture Notes in Computer Science, Vol. 3385. Springer, 124.
Dantzig G. B. 1951. Maximization of a linear function of variables subject to linear inequalities. In Activity Analysis of Production and Allocation – Proceedings of a Conference, Koopmans T., Ed. Cowles Commission Monograph, Vol. 13. Wiley, New York, 339347.
Devienne P., Lebègue P. and Routier J.-C. P. 1993. Halting problem of one binary horn clause is undecidable. In STACS 93, 10th Annual Symposium on Theoretical Aspects of Computer Science, Würzburg, Germany, February 25–27, 1993, Proceedings., Enjalbert P., Finkel A. and Wagner K. W., Eds. Lecture Notes in Computer Science, Vol. 665. Springer, 4857.
Holzbaur C. 1995. OFAI clp(Q,R) Manual. Tech. Rep. TR-95-09, Austrian Research Institute for Artificial Intelligence (ÖFAI), Schottengasse 3, A-1010 Vienna, Austria.
Jaffar J. and Maher M. J. 1994. Constraint logic programming: A survey. Journal of Logic Programming 19/20, 503582.
Jaffar J., Maher M. J., Marriott K. and Stuckey P. J. 1998. The semantics of constraint logic programs. Journal of Logic Programming 37 (1–3), 146.
Khachiyan L. 1979. A polynomial algorithm in linear programming. Soviet Mathematics–-Doklady 20, 191194.
Marcinkowski J. 1996. DATALOG SIRUPs uniform boundedness is undecidable. In Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science. 13–24.
Marriott K. and Stuckey P. J. 1998. Programming With Constraints: An Introduction. The MIT Press.
Pheidas T. 2000. An effort to prove that the existential theory of inline-graphic
${\mathbb Q}$
is undecidable. In Hilbert's Tenth Problem: Relations with Arithmetic and Algebraic Geometry, Denef J., Lipshitz L., Pheidas T. and Geel J. V., Eds. Contemporary Mathematics 270, 237–252. American Mathematic Society, 2000. MR 2001m:03085.
Podelski A. and Rybalchenko A. 2004. A complete method for the synthesis of linear ranking functions. In Verification, Model Checking, and Abstract Interpretation, 5th International Conference, Venice, January 11–13, 2004, Proceedings, Steffen B. and Levi G., Eds. Lecture Notes in Computer Science, Vol. 2937. Springer, 239–251.
Renegar J. 1992. On the computational complexity and geometry of the first-order theory of the reals. Journal of Symbolic Computation 13 (3), 255352.
Schrijver A. 1986. Theory of Linear and Integer Programming. Wiley.
Serebrenik A. and Mesnard F. 2004. On termination of binary CLP programs. In Logic Based Program Synthesis and Transformation, 14th International Symposium, LOPSTR, Verona, Italy, August 26–28, 2004, Revised Selected Papers, Etalle S., Ed. Lecture Notes in Computer Science, Vol. 3573. Springer, 231–244.
SICS. 2005. SICStus User Manual. Version 3.12.3. Swedish Institute of Computer Science.
Sohn K. and Van Gelder A. 1991. Termination detection in logic programs using argument sizes. In Proceedings of the Tenth ACM SIGACT-SIGART-SIGMOD Symposium on Principles of Database Systems. ACM Press, 216–226.
Tarski A. 1931. Sur les ensembles définissables de nombres réels. Fundamenta Mathematicae 17, 210239.
Tarski A. 1951. A Decision Method for Elementary Algebra and Geometry, 2nd ed.University of California Press.
Tiwari A. 2004. Termination of linear programs. In Computer-Aided Verification, CAV, Alur R. and Peled D., Eds. Lecture Notes on Computer Science, Vol. 3114. Springer, 7082.
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Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
  • URL: /core/journals/theory-and-practice-of-logic-programming
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