Abstract
Termination analysis is often performed over the abstract domains of monotonicity constraints or of size change graphs. First, the transition relation for a given program is approximated by a set of descriptions. Then, this set is closed under a composition operation. Finally, termination is determined if all of the idempotent loop descriptions in this closure have (possibly different) ranking functions. This approach is complete for size change graphs: An idempotent loop description has a ranking function if and only if it has one which indicates that some specific argument decreases in size. In this paper we generalize the size change criteria for size change graphs which are not idempotent. We also illustrate that proving termination with monotonicity constraints is more powerful than with size change graphs and demonstrate that the size change criteria is incomplete for monotonicity constraints. Finally, we provide a complete termination test for monotonicity constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brodsky, A., Sagiv, Y.: Inference of monotonicity constraints in Datalog programs. In: Proceedings of the Eighth ACM SIGACT-SIGART-SIGMOD Symposium on Principles of Database Systems, pp. 190–199 (1989)
Codish, M., Taboch, C.: A semantic basis for the termination analysis of logic programs. The Journal of Logic Programming 41(1), 103–123 (1999)
Dershowitz, N., Lindenstrauss, N., Sagiv, Y., Serebrenik, A.: A general framework for automatic termination analysis of logic programs. Applicable Algebra in Engineering, Communication and Computing 12(1-2), 117–156 (2001)
Frederiksen, C.C.: A simple implementation of the size-change termination principle. Technical Report D-442, DIKU, Copenhagen University, Denmark (2001)
Frobenius, G.: Über endliche gruppen. In: Sitzungsber. Preuss. Akad. Wiss., Berlin, pp. 163–194 (1895)
Gabbrielli, M., Giacobazzi, R.: Goal independency and call patterns in the analysis of logic programs. In: Proceedings of the Ninth ACM Symposium on Applied Computing, pp. 394–399. ACM Press, New York (1994)
Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proceedings of POPL 2001. ACM SIGPLAN Notices, vol. 36(3), pp. 81–92 (2001)
Lindenstrauss, N., Sagiv, Y.: Automatic termination analysis of logic programs. In: Naish, L. (ed.) Proceedings of the Fourteenth International Conference on Logic Programming, Leuven, Belgium, pp. 63–77. MIT Press, Cambridge (1997)
Lindenstrauss, N., Sagiv, Y., Serebrenik, A.: Termilog: A system for checking termination of queries to logic programs. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 444–447. Springer, Heidelberg (1997)
Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004)
Ramsey, F.: On a problem of formal logic. In: Proceedings London Mathematical Society, vol. 30, pp. 264–286 (1930)
Thiemann, R., Giesl, J.: Size-change termination for term rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 264–278. Springer, Heidelberg (2003)
Wahlstedt, D.: Detecting termination using size-change in parameter values. Master’s thesis, Göteborgs Universitet (2000), http://www.cs.chalmers.se/~davidw/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Codish, M., Lagoon, V., Stuckey, P.J. (2005). Testing for Termination with Monotonicity Constraints. In: Gabbrielli, M., Gupta, G. (eds) Logic Programming. ICLP 2005. Lecture Notes in Computer Science, vol 3668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11562931_25
Download citation
DOI: https://doi.org/10.1007/11562931_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29208-1
Online ISBN: 978-3-540-31947-4
eBook Packages: Computer ScienceComputer Science (R0)