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Proof and System-Reliability pp 79–135Cite as

Computability and Complexity from a Programming Perspective

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Part of the book series: NATO Science Series ((NAII,volume 62))

Abstract

A programming approach to computability and complexity theory yields proofs of central results that are sometimes more natural than the classical ones; and some new results as well. These notes contain some high points from the recent book [14], emphasising what is different or novel with respect to more traditional treatments. Topics include:

  • Kleene’s s-m-n theorem applied to compiling and compiler generation.

  • Proof that constant time factors do matter: for a natural computation model, problems solvable in linear time have a proper hierarchy, ordered by coefficient values. (In contrast to the “linear speedup” property of Turing machines.)

  • Results on which problems possess optimal algorithms, including Levin’s Search theorem (for the first time in book form).

  • Characterisations in programming terms of a wide range of complexity classes. These are intrinsic: without externally imposed space or time computation bounds.

  • Boolean program problems complete for PTIME, NPTIME, PSPACE.

This research was partially supported by the Danish Natural Science Research Council (DART project), and the Esprit Atlantique project.

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References

  1. Andersen, N. and Jones, N. D., Generalizing Cook’s construction to imperative stack programs, Lecture Notes in Computer Science 812, pp. 1–18, Springer-Verlag, 1994.

    Google Scholar 

  2. Cook, S. A., Linear-time simulation of deterministic two-way pushdown automata, Information Processing (IFIP) 71, C.V. Freiman, (ed.), North-Holland, pp. 75–80, 1971.

    Google Scholar 

  3. Cook, S. A., Characterizations of pushdown machines in terms of time-bounded computers. Journal of the ACM 18 (1971), 4–18.

    Article  MATH  Google Scholar 

  4. Cook, S. A., The complexity of theorem-proving procedures, Proceedings Third Symposium on the Theory of Computing, pp. 151–158, ACM Press, 1971

    Google Scholar 

  5. Ben-Amram, A. and Jones, N. D. A precise version of a time hierarchy theorem. Fundamenta Informaticae, vol. 38, pp. 1–15. 1999.

    MathSciNet  Google Scholar 

  6. Girard, J.-Y. and Lafont, Y. and Taylor, P. Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science Cambridge University Press, 1989.

    Google Scholar 

  7. Goerdt, A. Characterizing complexity classes by general recursive definitions in higher types. Information and Computation 101 (1992), 201–218.

    Article  MathSciNet  Google Scholar 

  8. Goerdt, A. Characterizing complexity classes by higher type primitive recursive definitions. Theoretical Computer Science 101 (1992), 45–66.

    Article  MathSciNet  Google Scholar 

  9. Goerdt, A. and Seidl, H. Characterizing complexity classes by higher type primitive recursive definitions, Part II. Proceedings 6th International Meeting for Young Computer Scientists, Lecture Notes in Computer Science 464 (1990), 148–158.

    MathSciNet  Google Scholar 

  10. Hutton, G. A tutorial on the universality and expressiveness of fold. Journal of Functional Programming 1 (1):1–17 (1953).

    Google Scholar 

  11. Jones, N. D., Space-bounded reducibility among combinatorial problems, Journal of Computer and System Science, vol. 11, pp. 68–85, 1975.

    Article  Google Scholar 

  12. Jones, N. D., The Expressive Power of Higher-order Types or, Life without CONS, Journal of Functional Programming accepted for publication, 2000.

    Google Scholar 

  13. Jones, N. D., A note on linear-time simulation of deterministic two-way pushdown automata, Information Processing Letters vol. 6, pp. 110–112, 1977.

    Article  MATH  Google Scholar 

  14. Jones, N. D., Constant time factors do matter. In Steven Homer, editor, STOC ’93. Symposium on Theory of Computing, pages 602–611. ACM Press, 1993.

    Google Scholar 

  15. Jones, N. D., Computability and Complexity from a Programming Perspective. The MIT Press, 1997.

    MATH  Google Scholar 

  16. Jones, N. D. and Gomard, C. and Sestoft, P. Partial Evaluation and Automatic Program Generation. Prentice-Hall International, 1993.

    MATH  Google Scholar 

  17. Jones, N. D., Logspace and Ptime characterized by programming languages. Theoretical Computer Science, 1998.

    Google Scholar 

  18. Jones, N. D., and Muchnick, S. Even simple programs are hard to analyze. Journal of the Association for Computing Machinery, 24(2):338–350, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  19. Jones, N. D., and Muchnick, S. Complexity of finite memory programs with recursion. Journal of the Association for Computing Machinery, 25(2):312–321, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  20. Kfoury, A. J. and Moll, R. N. and Arbib, M. A. A Programming Approach to Computability. Texts and monographs in Computer Science. Springer-Verlag, 1982.

    Book  MATH  Google Scholar 

  21. Voda, P. Subrecursion as Basis for a Feasible Programming language. In Steven Homer, editor, Logic in Comp. Science September 94. Lecture Notes in Computer Science 933, Springer Verlag 1995.

    Google Scholar 

  22. Voda, P. A simple ordinal recursive normalization of Gödel’s T. Computer Science Logic, Lecture Notes in Computer Science 1414 (1997), 491–509.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. DIKU, University of Copenhagen, Denmark

    Neil D. Jones

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  1. Neil D. Jones
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität, München, Germany

    Helmut Schwichtenberg

  2. Institut für Informatik, Technische Universität, München, Germany

    Ralf Steinbrüggen

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© 2002 Springer Science+Business Media Dordrecht

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Jones, N.D. (2002). Computability and Complexity from a Programming Perspective. In: Schwichtenberg, H., Steinbrüggen, R. (eds) Proof and System-Reliability. NATO Science Series, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0413-8_4

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  • DOI: https://doi.org/10.1007/978-94-010-0413-8_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0608-1

  • Online ISBN: 978-94-010-0413-8

  • eBook Packages: Springer Book Archive

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