Linear time hierarchies for a functional language machine model

  • Eva Rose
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1058)


In STOC 93, Jones sketched the existence of a hierarchy within problems decidable in linear time by a first-order functional language based on tree-structured data (F), as well as for an extension of that language based on graph-structured data (Fsu).

We consider the Categorical Abstract Machine (CAM), a canonical machine model for implementing higher order functional languages. We show the existence of such a hierarchy for the CAM based on tree-structured data (without selective updating facilities), as well as in the case of graphstructured data (with selective updating). In conclusion we establish two local robustness results where first-order functional programs and higher order functional programs define the same class of linear-time decidable problems.


linear time complexity hierarchy CAM operational semantics functional languages selective update structured data 


  1. [BA95]
    A. M. Ben-Amram. Pointer machines and pointer algorithms: an annotated bibliography. Diku-rapport 95/21, DIKU (Department of Computer Science), University of Copenhagen, September 1995.Google Scholar
  2. [BAJ95]
    A. M. Ben-Amram and N. D. Jones. Complexity-theoretic advantages of structured programs and structured data. Personal communication, October 1995.Google Scholar
  3. [BvEG+87]
    H. P. Barendregt, M. C. D. J. van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasmeijer, and M. R. Sleep. Term graph rewriting. In J. W. de Bakker, A. J. Nijman, and P. C. Treleaven, editors, PARLE '87-Parallel Architectures and Languages Europe vol. II, number 256 in LNCS, pages 141–158, Eindhoven, The Netherlands, June 1987. Springer-Verlag.Google Scholar
  4. [CCM87]
    G. Cousineau, P.-L. Curien, and M. Mauny. The categorical abstract machine. Science of Computer Programming, 8:173–202, 1987.CrossRefGoogle Scholar
  5. [CR+91]
    W. Clinger, J. Rees, et al. Revised 4 Report on the Algorithmic Language Scheme, November 1991.Google Scholar
  6. [Cur90]
    P.-L. Curien. An abstract framework for environment machines. Theoretical Computer Science, 82(2):389–402, 1990.Google Scholar
  7. [DH94]
    C. Dahl and M. Hessellund. Determining the constant coefficients in a time hierarchy. Student report 94-2-2, DIKU (University of Copenhagen), Department of Computer Science, Universitetsparken 1, DK-2100 Copenhagen Ø, Denmark, February 1994.Google Scholar
  8. [GS85]
    Y. Gurevich and S. Shelah. Nearly linear time. In Logic at Botik, volume 363 of LNCS, pages 108–118. Springer-Verlag, 1985.Google Scholar
  9. [Han91]
    J. Hannan. Making abstract machines less abstract. In Functional Programming Languages and Computer Architecture, number 523 in LNCS, pages 618–635. Springer-Verlag, August 1991.Google Scholar
  10. [Jon93]
    N. D. Jones. Constant time factors do matter. In Steven Homer, editor, STOC '93. Symposium on Theory of Computing, pages 602–611. ACM Press, 1993.Google Scholar
  11. [Jon94]
    N. D. Jones. Program speedups in theory and practice. In B. Pehrson and I. Simon, editors, 13th World Computer Congress 94, volume 1. IFIP, Elsevier Science B.V. (North-Holland), 1994.Google Scholar
  12. [Kah87]
    G. Kahn. Natural semantics. Rapport de Recherche 601, INRIA, Sophia-Antipolis, France, February 1987.Google Scholar
  13. [M+90]
    A. R. Meyer et al. Algorithm and Complexity, volume A of Handbook of Theoretical Computer Science. Elsevier Science Publishers B.V., 1990.Google Scholar
  14. [Pap94]
    C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.Google Scholar
  15. [PH87]
    R. Paige and F. Henglein. Mechanical translation of set theoretic problem specifications into efficient ram code — a case study. In Lisp and Symbolic Computation, volume 4, pages 207–232. North-Holland, August 1987.Google Scholar
  16. [Plo81]
    G. D. Plotkin. A structural approach to operational semantics. Technical Report FN-19, DAIMI, Aarhus University, Aarhus, Denmark, 1981.Google Scholar
  17. [Reg94]
    K. Regan. Linear speed-up, information vicinity, and finite-state machines. In IFIP proceedings. North-Holland, 94.Google Scholar
  18. [Ros96]
    E. Rose. Linear time hierarchies for a functional language machine model. Student report, DIKU, Department of Computer Science, Universitetsparken 1, 2100 Copenhagen Ø, Denmark, 1996.Google Scholar
  19. [W+87]
    P. Weis et al. The CAML Reference Manual. INRIA-ENS, version 2.5 edition, December 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Eva Rose
    • 1
  1. 1.DIKUUniversity of CopenhagenDenmark

Personalised recommendations