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Deriving linear size relations for logic programs by abstract interpretation

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Abstract

We propose an automatic method for derivinglinear size relations, which specify, with respect to some given norm, linear relationships between the sizes of the arguments of atoms in the least Herbrand model of a definite Horn clause program. The method is presented as an application of abstract interpretation. Its abstract domain consists of affine subspaces or linear varieties, and operations on elements of the domain are expressed in terms of operations from linear algebra. The main application of the technique is situated in automatic termination analysis. Others are complexity and granularity analysis and the specialisation of constraints in constraint logic languages.

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Authors and Affiliations

  1. Department of Computer Science, K. U. Leuven, Celestijnenlaan 200A, B-3001, Heverlee, Belgium

    Danny De Schreye & Kristof Verschaetse

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  1. Danny De Schreye
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  2. Kristof Verschaetse
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Additional information

Work partly supported by Esprit Project Compulog II, Contract No. 6810.

Senior research associate of the Belgian National Fund for Scientific Research.

Partly supported by Esprit Project Compulog, Contract No. 3012 and by RFO/AI/02 (Belgium).

Danny De Schreye, Ph. D.: He is a professor at the Department of Computer Science of the Katholieke Universiteit Leuven and a senior research associate of the Belgian National Fund for Scientific Research. He obtained his Ph. D from K. U. Leuven in 1983, on the topic of operator algebras. His research interests are in the field of Logic Programming, and include program transformation and termination, knowledge representation and reasoning, and constraint programming.

Kristof Verschaetse, Ph. D.: He obtained his Ph. D from K. U. Leuven in 1992. His main research topic is termination analysis of logic programs, including formal characterisation of terminating programs and the development of verification tools. Other interests are object oriented analysis and design, and the integration of constraint programming in object orientation.

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De Schreye, D., Verschaetse, K. Deriving linear size relations for logic programs by abstract interpretation. New Gener Comput 13, 117–154 (1995). https://doi.org/10.1007/BF03038311

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  • DOI: https://doi.org/10.1007/BF03038311

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