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On Lexicographic Termination Ordering with Space Bound Certifications

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Perspectives of System Informatics (PSI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2244))

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Abstract

We propose a method to analyse the program space complexity, based on termination orderings. This method can be implemented to certify the runspace of programs. We demonstrate that the class of functions computed by first order functional programs over free algebras which terminate by Lexicographic Path Ordering and admit a polynomial quasi-interpretation, is exactly the class of functions computable in polynomial space.

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References

  1. S. Bellantoni and S. Cook. A new recursion-theoretic characterization of the polytime functions. Computational Complexity, 2:97–110, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Benzinger. Automated complexity analysis of NUPRL extracts. PhD thesis, Cornell University, 1999.

    Google Scholar 

  3. G. Bonfante, A. Cichon, J-Y Marion, and H. Touzet. Complexity classes and rewrite systems with polynomial interpretation. In Computer Science Logic, 12th International Workshop, CSL’98, volume 1584 of Lecture Notes in Computer Science, pages 372–384, 1999.

    Google Scholar 

  4. A. Chandra, D. Kozen, and L. Stockmeyer. Alternation. Journal of the ACM, 28:114–133, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Cobham. The intrinsic computational difficulty of functions. In Y. Bar-Hillel, editor, Proceedings of the International Conference on Logic, Methodology, and Philosophy of Science, pages 24–30. North-Holland, Amsterdam, 1962.

    Google Scholar 

  6. R. Constable and al. Implementing Mathematics with the Nuprl Development System. Prentice-Hall, 1986. http://www.cs.cornell.edu/Info/Projects/NuPrl/nuprl.html.

  7. K. Crary and S. Weirich. Ressource bound certification. In ACM SIGPLANSIGACT symposium on Principles of programming languages, POPL, pages 184–198, 2000.

    Google Scholar 

  8. N. Dershowitz and J-P Jouannaud. Handbook of Theoretical Computer Science vol.B, chapter Rewrite systems, pages 243–320. Elsevier Science Publishers B. V. (North-Holland), 1990.

    Google Scholar 

  9. A. Goerdt. Characterizing complexity classes by higher type primitive recursive definitions. Theoretical Computer Science, 100(1):45–66, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Hofbauer. Termination proofs with multiset path orderings imply primitive recursive derivation lengths. Theoretical Computer Science, 105(1):129–140, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Hofmann. Linear types and non-size-increasing polynomial time computation. In Proceedings of the Fourteenth IEEE Symposium on Logic in Computer Science (LICS’99), pages 464–473, 1999.

    Google Scholar 

  12. M. Hofmann. A type system for bounded space and functional in-place update. In European Symposium on Programming, ESOP’00, volume 1782 of Lecture Notes in Computer Science, pages 165–179, 2000.

    Google Scholar 

  13. N. Immerman. Descriptive Complexity. Springer, 1999.

    Google Scholar 

  14. N. Jones. The Expressive Power of Higher order Types or, Life without CONS. to appear, 2000.

    Google Scholar 

  15. S. Kamin and J-J Lévy. Attempts for generalising the recursive path orderings. Technical report, Univerity of Illinois, Urbana, 1980. Unpublished note.

    Google Scholar 

  16. M. S. Krishnamoorthy and P. Narendran. On recursive path ordering. Theoretical Computer Science, 40(2–3):323–328, October 1985.

    Article  MATH  MathSciNet  Google Scholar 

  17. D.S. Lankford. On proving term rewriting systems are noetherien. Technical Report MTP-3, Louisiana Technical University, 1979.

    Google Scholar 

  18. D. Leivant. Predicative recurrence and computational complexity I: Word recurrence and poly-time. In Peter Clote and Jeffery Remmel, editors, Feasible Mathematics II, pages 320–343. Birkhäuser, 1994.

    Google Scholar 

  19. D. Leivant and J-Y Marion. Ramified recurrence and computational complexityII: substitution and poly-space. In L. Pacholski and J. Tiuryn, editors, Computer Science Logic, 8th Workshop, CSL’94, volume 933 of Lecture Notes in Computer Science, pages 486–500, Kazimierz,Poland, 1995. Springer.

    Google Scholar 

  20. J-Y Marion. Complexité implicite des calculs, de la théorie à la pratique, 2000. Habilitation.

    Google Scholar 

  21. J-Y Marion and J-Y Moyen. Efficient first order functional program interpreter with time bound certifications. In LPAR, volume 1955 of Lecture Notes in Computer Science, pages 25–42. Springer, Nov 2000.

    Google Scholar 

  22. D.B. Thompson. Subrecursiveness: machine independent notions of computability in restricted time and storage. Math. System Theory, 6:3–15, 1972.

    Article  MATH  Google Scholar 

  23. A. Weiermann. Termination proofs by lexicographic path orderings yield multiply recursive derivation lengths. Theoretical Computer Science, 139:335–362, 1995.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Loria, Calligramme project, B.P. 239, 54506, Vandœuvre-lès-Nancy Cedex, France

    Guillaume Bonfante, Jean-Yves Marion & Jean-Yves Moyen

Authors
  1. Guillaume Bonfante
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  2. Jean-Yves Marion
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  3. Jean-Yves Moyen
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Editor information

Editors and Affiliations

  1. Informatics and Mathematical Modelling, Technical University of Denmark, Bldg.322, 106-108, Richard Petersens Plads, 2800, Lyngby, Denmark

    Dines Bjørner

  2. Computer Science Department, Technical University of Munich, Arcisstr.21, 80290, Munich, Germany

    Manfred Broy

  3. A.P.Ershov Institute of Informatics Systems, Acad.Lavrentjev ave.,6, 630090, Novosibirsk, Russia

    Alexandre V. Zamulin

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© 2001 Springer-Verlag Berlin Heidelberg

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Bonfante, G., Marion, JY., Moyen, JY. (2001). On Lexicographic Termination Ordering with Space Bound Certifications. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 2001. Lecture Notes in Computer Science, vol 2244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45575-2_46

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  • DOI: https://doi.org/10.1007/3-540-45575-2_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43075-9

  • Online ISBN: 978-3-540-45575-2

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