Polynomial interpretations as a basis fo
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Polynomial interpretations as a basis fo
Polynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo -KampReport cw 412, Revised version. August 2007Katholieke Universiteit Leuven Department of Computer Science Celestijnenlaan 200A - B-3001 Heverlee (Belgium)Polynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen. Danny De Schreye Jurgen Giesl, and Peter Sc Polynomial interpretations as a basis fo hneider-KampReport CWJJ2, Revised version, August 2007Department of Computer Science. K.Ư.LeuvenAbstractThis paper introduces a new technique for termPolynomial interpretations as a basis fo
inat ion analysis of definite logic programs (LPs) liased on polynomial interpretations. The principle of this technique is to map each function and pPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo nomial interpretations can 1st 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 termina Polynomial interpretations as a basis fo tion analysis to the context of polynomial interpretations. We propose a constraint based approach for automatically generating polynomial interpretatPolynomial interpretations as a basis fo
ions that satisfy the termination conditions. Based on tills approach, we implement a new tool, called Polytool, for automatic termination analysis ofPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo tion Analysis of Logic ProgramsNíanh Thang Nguyen1. Danny De Schreye1, Jurgen Gicsl2, and Peter Schneider- K amp21 Department of Computer Science, K.U.Lcuven Cclcstijnciihuui 200A. B-3001, llcvcrlce, Belgium {ManhThang-Nguycn, Danny.DcSchrcyeJiScs.kulcnvcn.ac.be2 Department of Computer Science. RWTH Polynomial interpretations as a basis fo Aachen Ahornstr. 55, D-520S6 Aachen, Germany {gicsl, pskjiiinformatik.iwth-aachen.dcAbstract. This paper introduces a new technique for termination aPolynomial interpretations as a basis fo
nalysis of definite logic programs based on polynomial interpretations, rhe principle of this technique is to map each function and predicate symbol tPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo tions carr be seen as a direct generalisation of the traditional techniques in termination analysis of Li’s, where (semi-)lincar 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 Polynomial interpretations as a basis fo the context of polynomial interpretations. We propose a constraint based approach for automatically generating polynomial interpretations that satisfPolynomial interpretations as a basis fo
y the termination conditions. Based orr this approach, we implement a new tool, namely Polytool, for automatic termination analysis of logic programs.Polynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo rogram correctness. A termination proof is mostly based on a mapping from computational states to some well-founded ordered set. Termination is guaranteed if the mapped values of the encountered states during a computation, under this mapping, decrease w.r.t. the ordering.For Logic Programming (LP). Polynomial interpretations as a basis fo termination analysis Ls done by mapping terms ami atoms to a well-founded set of natural numbers by means of norms and level mappings. Proving terminPolynomial interpretations as a basis fo
ation is based on the search for a suitable norm and level mapping such that the mapped value of the initial predicate call is bounded and of the runnPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo on verifying the decrease in size of (mutually) recursive predicate calls,which correspond to the loops that the execution passes through.Until now. most termination techniques in LP are based on the use of semi-linear norms and level mappings, which measure the size of each term or atom as a linear Polynomial interpretations as a basis fo combination of its subterms. For example, the Hasta La Vista system '31] infers one specific semi-linear norm ami the TerminWeb analyser [34] uses aPolynomial interpretations as a basis fo
combinat ion of several semi-linear norms for termination analysis. A restriction of semi-linear norms is that a lot of examples require more powerfulPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo erivative of a function in some variable u. This example was first introduced in [13] (see also [10]).Example 1 (der).d(Polynomial interpretations as a basis fo
e first argument of d/2 as an input argument ami the second as an output.Doing this on the basis of a semi-linear norm and level mapping is impossiblePolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo at there exists such a semi-linear norm |.| and level mapping |.| of general forms such that: II «■ = c.- II''-t M = ứ + tfllh II + jf/IIM. ló * M = fs +/ÍIIGII + fi iLdl.II Jer(f )|| =4- /;'||í||, |d(QUs)| = d0 + df |t/|| + dgỊỊf.gịị where t, tj, tg are termsandami nt arc non-negative inte-gers. Ap Polynomial interpretations as a basis fo plying the genend constraint based method in [12] shows a contradiction: the system of inequalities that is set up from the acceptability condition isPolynomial interpretations as a basis fo
unsolvable. A complete proof can be found in [25]. Of course this only proves that one particular approach is unable to prove termination on the basiPolynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo Using polynomial interpretations as a basis for ordering terms in TRSs was first introduced by Lankford in [22]. It is currently one of the best known and most widely used techniques in TRS termination analysis.We develop the approach within an LP context. We redefine and extend several known conce Polynomial interpretations as a basis fo pts ami results from LP termination analysis to polynomial interpretations. We show how polynomial interpretations can be seen as a direct generalisatPolynomial interpretations as a basis fo
ion of currently used techniques in LP termination based on (semi-)linear norms and linear level-mappings. As one would expect, the generalisation is Polynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider- Polynomial interpretations as a basis fo d ‘abstract level mapping’ [35]. We show that under this approach, examples as the2Polynomial Interpretations as a Basis for Termination Analysis of Logic ProgramsManh Thang Nguyen, Danny De Schreye Jurgen Giesl, and Peter Schneider-Gọi ngay
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