Real or natural number interpretation and their effect on complexity
Interpretation methods have been introduced in the 70s by Lankford [1] in rewriting theory to prove termination. Actually, as shown by Bonfante et al. [2], an interpretation of a program induces a bound on its complexity. However, Lankford's original analysis depends deeply on the Archimedean p...
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| Vydané v: | Theoretical computer science Ročník 585; s. 25 - 40 |
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Elsevier B.V
20.06.2015
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | Interpretation methods have been introduced in the 70s by Lankford [1] in rewriting theory to prove termination. Actually, as shown by Bonfante et al. [2], an interpretation of a program induces a bound on its complexity. However, Lankford's original analysis depends deeply on the Archimedean property of natural numbers. This goes against the fact that finding a real interpretation can be solved by Tarski's decision procedure over the reals (as described by Dershowitz in [3]), and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (well-)ordering of N used to bound the complexity of programs. We prove that one may take benefit from the best of both worlds: the complexity analysis still holds even with real numbers. The reason lies in a deep algebraic property of polynomials over the reals. We illustrate this by two characterizations, one of polynomial time and one of polynomial space. |
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| AbstractList | Interpretation methods have been introduced in the 70s by Lankford [1] in rewriting theory to prove termination. Actually, as shown by Bonfante et al. [2], an interpretation of a program induces a bound on its complexity. However, Lankford's original analysis depends deeply on the Archimedean property of natural numbers. This goes against the fact that finding a real interpretation can be solved by Tarski's decision procedure over the reals (as described by Dershowitz in [3]), and consequently interpretations are usually chosen over the reals rather than over the integers. Doing so, one cannot use anymore the (good) properties of the natural (well-)ordering of N used to bound the complexity of programs. We prove that one may take benefit from the best of both worlds: the complexity analysis still holds even with real numbers. The reason lies in a deep algebraic property of polynomials over the reals. We illustrate this by two characterizations, one of polynomial time and one of polynomial space. |
| Author | Bonfante, Guillaume Deloup, Florian Henrot, Antoine |
| Author_xml | – sequence: 1 givenname: Guillaume surname: Bonfante fullname: Bonfante, Guillaume email: Guillaume.Bonfante@loria.fr organization: Université de Lorraine – LORIA, Nancy, France – sequence: 2 givenname: Florian surname: Deloup fullname: Deloup, Florian organization: Université Paul Sabatier, Toulouse – IMT, France – sequence: 3 givenname: Antoine surname: Henrot fullname: Henrot, Antoine organization: Université de Lorraine – IECN, Nancy, France |
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| Keywords | Term rewriting Polynomial interpretation Algebraic geometry Implicit computational complexity |
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| References | Stengle (br0190) 1973; 207 Huet (br0230) 1980; 27 Avanzini, Moser (br0120) 2008; vol. 4989 Hofbauer (br0300) 2006; vol. 4098 Marion, Péchoux (br0250) 2006; vol. 3945 Marion, Péchoux (br0270) 2009; 10 Arts, Giesl (br0160) 2000; 236 Bonfante, Cichon, Marion, Touzet (br0020) 2001; 11 Hofbauer, Lautemann (br0100) 1989 Lucas (br0260) 2007 Moser, Schnabl (br0140) 2008; vol. 5117 Huet, Oppen (br0040) 1980 Dershowitz (br0030) 1979 Baader, Nipkow (br0210) 1998 Rosen (br0240) 1973; 20 Tarski (br0050) 1951 Lucas, Peña (br0180) 2008 TeReSe (br0220) 2003; vol. 55 Lucas (br0080) 2006; 17 Hirokawa, Moser (br0170) 2008; vol. 5195 Hong, Jakus (br0070) 1998; 21 Neurauter, Middeldorp (br0090) 2010; vol. 6 Marion, Péchoux (br0200) 2008 Basu, Pollack, Roy (br0060) 2003 Lankford (br0010) 1979 Cichon, Lescanne (br0110) 1992; vol. 607 Coste, Lombardi, Roy (br0280) 2001; 111 Avanzini, Eguchi, Moser (br0130) 2012; vol. 7705 Dal Lago, Martini (br0290) 2009 Hofbauer (br0150) 2001; vol. 2051 Dal Lago (10.1016/j.tcs.2015.03.004_br0290) 2009 Avanzini (10.1016/j.tcs.2015.03.004_br0130) 2012; vol. 7705 Neurauter (10.1016/j.tcs.2015.03.004_br0090) 2010; vol. 6 Rosen (10.1016/j.tcs.2015.03.004_br0240) 1973; 20 Dershowitz (10.1016/j.tcs.2015.03.004_br0030) 1979 Moser (10.1016/j.tcs.2015.03.004_br0140) 2008; vol. 5117 Bonfante (10.1016/j.tcs.2015.03.004_br0020) 2001; 11 Basu (10.1016/j.tcs.2015.03.004_br0060) 2003 Arts (10.1016/j.tcs.2015.03.004_br0160) 2000; 236 TeReSe (10.1016/j.tcs.2015.03.004_br0220) 2003; vol. 55 Marion (10.1016/j.tcs.2015.03.004_br0270) 2009; 10 Coste (10.1016/j.tcs.2015.03.004_br0280) 2001; 111 Huet (10.1016/j.tcs.2015.03.004_br0040) 1980 Baader (10.1016/j.tcs.2015.03.004_br0210) 1998 Hong (10.1016/j.tcs.2015.03.004_br0070) 1998; 21 Tarski (10.1016/j.tcs.2015.03.004_br0050) 1951 Hofbauer (10.1016/j.tcs.2015.03.004_br0100) 1989 Huet (10.1016/j.tcs.2015.03.004_br0230) 1980; 27 Avanzini (10.1016/j.tcs.2015.03.004_br0120) 2008; vol. 4989 Lucas (10.1016/j.tcs.2015.03.004_br0180) 2008 Lucas (10.1016/j.tcs.2015.03.004_br0080) 2006; 17 Lankford (10.1016/j.tcs.2015.03.004_br0010) 1979 Hofbauer (10.1016/j.tcs.2015.03.004_br0150) 2001; vol. 2051 Hirokawa (10.1016/j.tcs.2015.03.004_br0170) 2008; vol. 5195 Stengle (10.1016/j.tcs.2015.03.004_br0190) 1973; 207 Lucas (10.1016/j.tcs.2015.03.004_br0260) 2007 Hofbauer (10.1016/j.tcs.2015.03.004_br0300) 2006; vol. 4098 Marion (10.1016/j.tcs.2015.03.004_br0200) 2008 Cichon (10.1016/j.tcs.2015.03.004_br0110) 1992; vol. 607 Marion (10.1016/j.tcs.2015.03.004_br0250) 2006; vol. 3945 |
| References_xml | – year: 1979 ident: br0010 article-title: On proving term rewriting systems are Noetherian – volume: vol. 2051 start-page: 108 year: 2001 end-page: 121 ident: br0150 article-title: Termination proofs by context-dependent interpretations publication-title: Proceedings of the 12th International Conference on Rewriting Techniques and Applications – volume: 10 year: 2009 ident: br0270 article-title: Sup-interpretations, a semantic method for static analysis of program resources publication-title: ACM Trans. Comput. Log. – volume: vol. 5195 start-page: 364 year: 2008 end-page: 379 ident: br0170 article-title: Automated complexity analysis based on the dependency pair method publication-title: IJCAR – start-page: 349 year: 1980 end-page: 405 ident: br0040 article-title: Equations and rewrite rules: a survey publication-title: Formal Language Theory: Perspectives and Open Problems – volume: vol. 5117 start-page: 276 year: 2008 end-page: 290 ident: br0140 article-title: Proving quadratic derivational complexities using context dependent interpretations publication-title: Rewriting Techniques and Applications – volume: 111 start-page: 203 year: 2001 end-page: 256 ident: br0280 article-title: Dynamical method in algebra: effective nullstellensätze publication-title: Ann. Pure Appl. Logic – start-page: 43 year: 2008 end-page: 57 ident: br0180 article-title: Rewriting techniques for analysing termination and complexity bounds of safe programs publication-title: LOPSTR 08 – volume: 20 start-page: 160 year: 1973 end-page: 187 ident: br0240 article-title: Tree-manipulating systems and Church–Rosser theorems publication-title: J. ACM – year: 1951 ident: br0050 article-title: A Decision Method for Elementary Algebra and Geometry – volume: 207 start-page: 87 year: 1973 end-page: 97 ident: br0190 article-title: A nullstellensatz and a positivstellensatz in semialgebraic geometry publication-title: Math. Ann. – volume: vol. 7705 start-page: 280 year: 2012 end-page: 296 ident: br0130 article-title: A new order-theoretic characterisation of the polytime computable functions publication-title: Proceedings of the 10th Asian Symposium on Programming Languages and Systems – volume: vol. 6 start-page: 243 year: 2010 end-page: 258 ident: br0090 article-title: Polynomial interpretations over the reals do not subsume polynomial interpretations over the integers publication-title: RTA – year: 1998 ident: br0210 article-title: Term Rewriting and All That – volume: 21 start-page: 23 year: 1998 end-page: 38 ident: br0070 article-title: Testing positiveness of polynomials publication-title: J. Automat. Reason. – start-page: 79 year: 2008 end-page: 88 ident: br0200 article-title: Characterizations of polynomial complexity classes with a better intensionality publication-title: PPDP – volume: 236 start-page: 133 year: 2000 end-page: 178 ident: br0160 article-title: Termination of term rewriting using dependency pairs publication-title: Theoret. Comput. Sci. – volume: vol. 55 year: 2003 ident: br0220 article-title: Term Rewriting Systems publication-title: Cambridge Tracts in Theoretical Computer Science – start-page: 212 year: 1979 end-page: 215 ident: br0030 article-title: A note on simplification orderings publication-title: Inform. Process. Lett. – year: 2009 ident: br0290 article-title: Derivational complexity is an invariant cost model publication-title: Foundational and Practical Aspects of Resource Analysis – volume: vol. 4098 start-page: 328 year: 2006 end-page: 342 ident: br0300 article-title: Proving termination with matrix interpretations publication-title: Proceedings of the 17th International Conference on Rewriting Techniques and Applications – volume: 11 start-page: 33 year: 2001 end-page: 53 ident: br0020 article-title: Algorithms with polynomial interpretation termination proof publication-title: J. Funct. Programming – year: 2003 ident: br0060 article-title: Algorithms in Real Algebraic Geometry – volume: vol. 4989 start-page: 130 year: 2008 end-page: 146 ident: br0120 article-title: Complexity analysis by rewriting publication-title: FLOPS – volume: 27 start-page: 797 year: 1980 end-page: 821 ident: br0230 article-title: Confluent reductions: abstract properties and applications to term rewriting systems publication-title: J. ACM – start-page: 167 year: 1989 end-page: 177 ident: br0100 article-title: Termination proofs and the length of derivations publication-title: Proceedings of the 3rd International Conference on Rewriting Techniques and Applications – volume: 17 start-page: 49 year: 2006 end-page: 73 ident: br0080 article-title: On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting publication-title: Appl. Algebra Engrg. Comm. Comput. – volume: vol. 607 start-page: 139 year: 1992 end-page: 147 ident: br0110 article-title: Polynomial interpretations and the complexity of algorithms publication-title: Lecture Notes in Artificial Intelligence – start-page: 39 year: 2007 end-page: 50 ident: br0260 article-title: Practical use of polynomials over the reals in proofs of termination publication-title: PPDP 2007: Proceedings of the 9th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming – volume: vol. 3945 start-page: 163 year: 2006 end-page: 176 ident: br0250 article-title: Resource analysis by sup-interpretation publication-title: FLOPS – volume: vol. 6 start-page: 243 year: 2010 ident: 10.1016/j.tcs.2015.03.004_br0090 article-title: Polynomial interpretations over the reals do not subsume polynomial interpretations over the integers – volume: vol. 607 start-page: 139 year: 1992 ident: 10.1016/j.tcs.2015.03.004_br0110 article-title: Polynomial interpretations and the complexity of algorithms – volume: vol. 4989 start-page: 130 year: 2008 ident: 10.1016/j.tcs.2015.03.004_br0120 article-title: Complexity analysis by rewriting – start-page: 43 year: 2008 ident: 10.1016/j.tcs.2015.03.004_br0180 article-title: Rewriting techniques for analysing termination and complexity bounds of safe programs – volume: 207 start-page: 87 issue: 2 year: 1973 ident: 10.1016/j.tcs.2015.03.004_br0190 article-title: A nullstellensatz and a positivstellensatz in semialgebraic geometry publication-title: Math. Ann. doi: 10.1007/BF01362149 – volume: 27 start-page: 797 issue: 4 year: 1980 ident: 10.1016/j.tcs.2015.03.004_br0230 article-title: Confluent reductions: abstract properties and applications to term rewriting systems publication-title: J. ACM doi: 10.1145/322217.322230 – start-page: 79 year: 2008 ident: 10.1016/j.tcs.2015.03.004_br0200 article-title: Characterizations of polynomial complexity classes with a better intensionality – start-page: 212 year: 1979 ident: 10.1016/j.tcs.2015.03.004_br0030 article-title: A note on simplification orderings publication-title: Inform. Process. Lett. doi: 10.1016/0020-0190(79)90071-1 – volume: vol. 2051 start-page: 108 year: 2001 ident: 10.1016/j.tcs.2015.03.004_br0150 article-title: Termination proofs by context-dependent interpretations – year: 2003 ident: 10.1016/j.tcs.2015.03.004_br0060 – volume: 111 start-page: 203 year: 2001 ident: 10.1016/j.tcs.2015.03.004_br0280 article-title: Dynamical method in algebra: effective nullstellensätze publication-title: Ann. Pure Appl. Logic doi: 10.1016/S0168-0072(01)00026-4 – start-page: 167 year: 1989 ident: 10.1016/j.tcs.2015.03.004_br0100 article-title: Termination proofs and the length of derivations – year: 2009 ident: 10.1016/j.tcs.2015.03.004_br0290 article-title: Derivational complexity is an invariant cost model – year: 1979 ident: 10.1016/j.tcs.2015.03.004_br0010 – volume: 20 start-page: 160 issue: 1 year: 1973 ident: 10.1016/j.tcs.2015.03.004_br0240 article-title: Tree-manipulating systems and Church–Rosser theorems publication-title: J. ACM doi: 10.1145/321738.321750 – volume: 11 start-page: 33 issue: 1 year: 2001 ident: 10.1016/j.tcs.2015.03.004_br0020 article-title: Algorithms with polynomial interpretation termination proof publication-title: J. Funct. Programming doi: 10.1017/S0956796800003877 – volume: 17 start-page: 49 issue: 1 year: 2006 ident: 10.1016/j.tcs.2015.03.004_br0080 article-title: On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting publication-title: Appl. Algebra Engrg. Comm. Comput. doi: 10.1007/s00200-005-0189-5 – volume: 10 issue: 4 year: 2009 ident: 10.1016/j.tcs.2015.03.004_br0270 article-title: Sup-interpretations, a semantic method for static analysis of program resources publication-title: ACM Trans. Comput. Log. doi: 10.1145/1555746.1555751 – volume: 236 start-page: 133 issue: 1–2 year: 2000 ident: 10.1016/j.tcs.2015.03.004_br0160 article-title: Termination of term rewriting using dependency pairs publication-title: Theoret. Comput. Sci. doi: 10.1016/S0304-3975(99)00207-8 – volume: vol. 55 year: 2003 ident: 10.1016/j.tcs.2015.03.004_br0220 article-title: Term Rewriting Systems – year: 1998 ident: 10.1016/j.tcs.2015.03.004_br0210 – start-page: 39 year: 2007 ident: 10.1016/j.tcs.2015.03.004_br0260 article-title: Practical use of polynomials over the reals in proofs of termination – year: 1951 ident: 10.1016/j.tcs.2015.03.004_br0050 – volume: vol. 4098 start-page: 328 year: 2006 ident: 10.1016/j.tcs.2015.03.004_br0300 article-title: Proving termination with matrix interpretations – volume: vol. 3945 start-page: 163 year: 2006 ident: 10.1016/j.tcs.2015.03.004_br0250 article-title: Resource analysis by sup-interpretation – volume: vol. 7705 start-page: 280 year: 2012 ident: 10.1016/j.tcs.2015.03.004_br0130 article-title: A new order-theoretic characterisation of the polytime computable functions – volume: vol. 5117 start-page: 276 year: 2008 ident: 10.1016/j.tcs.2015.03.004_br0140 article-title: Proving quadratic derivational complexities using context dependent interpretations – start-page: 349 year: 1980 ident: 10.1016/j.tcs.2015.03.004_br0040 article-title: Equations and rewrite rules: a survey – volume: vol. 5195 start-page: 364 year: 2008 ident: 10.1016/j.tcs.2015.03.004_br0170 article-title: Automated complexity analysis based on the dependency pair method – volume: 21 start-page: 23 issue: 1 year: 1998 ident: 10.1016/j.tcs.2015.03.004_br0070 article-title: Testing positiveness of polynomials publication-title: J. Automat. Reason. doi: 10.1023/A:1005983105493 |
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| SubjectTerms | Algebra Algebraic geometry Complexity Implicit computational complexity Integers Number theory Polynomial interpretation Polynomials Real numbers Term rewriting |
| Title | Real or natural number interpretation and their effect on complexity |
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