Abstract
This paper introduces a new technique for termination analysis of definite logic programs based on polynomial interpretations. The principle of this technique is to map each function and predicate symbol to a polynomial over some domain of natural numbers, like it has been done in proving termination of term rewriting systems. Such polynomial interpretations can be seen as a direct generalisation of the traditional techniques in termination analysis of LPs, where (semi-) linear norms and level mappings are used. Our extension generalises these to arbitrary polynomials. We extend a number of standard concepts and results on termination analysis to the context of polynomial interpretations. We propose a constraint based approach for automatically generating polynomial interpretations that satisfy termination conditions.
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
Apt, K.R.: Logic programming. In: Handbook of theoretical computer science: formal models and semantics, vol. B, pp. 493–574. MIT Press, Cambridge (1990)
Bossi, A., Cocco, N., Fabris, M.: Proving termination of logic programs by exploiting term properties. In: TAPSOFT, vol. 2, pp. 153–180 (1991)
Contejean, E., Marché, C., Tomás, A.P., Urbain, X.: Mechanically proving termination using polynomial interpretations. J. Auto. Reason. (2005)
De Schreye, D., Decorte, S.: Termination of logic programs: the never-ending story. J. Log. Program. 19-20, 199–260 (1994)
De Schreye, D., Serebrenik, A.: Acceptability with general orderings. In: Computational Logic: Logic Programming and Beyond, pp. 187–210. Springer, Heidelberg (2002)
Decorte, S., De Schreye, D., Vandecasteele, H.: Constraint based automatic termination analysis of logic programs. ACM Trans. Program. Lang. Syst 21(6), 1137–1195 (1999)
Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1-2), 69–116 (1987)
Comon, H., Jouannaud, J.-P. (eds.): TCS School 1993. LNCS, vol. 909, pp. 16–26. Springer, Heidelberg (1995)
Falaschi, M., Levi, G., Martelli, M., Palamidessi, C.: Declarative modeling of the operational behaviour of logic languages. Theor. Comput. Sci. 63(3), 289–318 (1989)
Giesl, J.: Generating polynomial orderings for termination proofs. In: Hsiang, J. (ed.) RTA 1995. LNCS, vol. 914, pp. 426–431. Springer, Heidelberg (1995)
Janssen, G., Bruynooghe, M.: Deriving descriptions of possible values of program variables by means of abstract interpretation. J. Log. Program. 13(2,3), 205–258 (1992)
Lankford, D.S.: On proving term rewriting systems are noetherian. Technical report, Mathematics Department, Louisiana Tech. University, Ruston, LA (1979)
Lloyd, J.W.: Foundations of Logic Programming. Springer, Berlin (1987)
Nguyen, M.T., De Schreye, D.: Polynomial interpretations as a basis for termination analysis of logic programs. Technical report, Department of Computer Science, K.U.Leuven, Belgium (2005)
Serebrenik, A.: Termination Analysis of Logic Programs. PhD thesis, Department of Computer Science, K.U.Leuven, Belgium (2003)
Steinbach, J.: Generating polynomial orderings. Inf. Process. Lett. 49(2), 85–93 (1994)
Verschaetse, K., De Schreye, D.: Deriving termination proofs for logic programs, using abstract procedures. In: Proceedings 8th ICLP, pp. 301–315 (1991)
Zantema, H.: Termination. In: Terese, Term Rewriting Systems, ch. 6. Cambridge University Press, Cambridge (2003)
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
Nguyen, M.T., De Schreye, D. (2005). Polynomial Interpretations as a Basis for Termination Analysis of Logic Programs. 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_24
Download citation
DOI: https://doi.org/10.1007/11562931_24
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)