Syntactic characterization in Lisp of the polynomial complexity classes and hierarchy

  • Salvatore Caporaso
  • Michele Zito
  • Nicola Galesi
  • Emanuele Covino
Regular Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1203)


The definition of a class C of functions is syntactic if membership to C can be decided from the construction of its elements. Syntactic characterizations of PTIMEF, of PSPACEF, of the polynomial hierarchy PH, and of its subclasses Δ n p are presented. They are obtained by progressive restrictions of recursion in Lisp, and may be regarded as predicative according to a foundational point raised by Leivant.


Recursive Call Polynomial Hierarchy Primitive Recursive Primitive Recursive Function Syntactic Characterization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Bellantoni and S. Cook, A new recursive characterization of the polytime funcions, in 24th Annual ACM STOC (1992) 283–293.Google Scholar
  2. 2.
    S. Caporaso, Safe Turing machines, Grzegorczyk classes and Polytime (to appear on Intern. J. Found. Comp. Sc.).Google Scholar
  3. 3.
    S. Caporaso and M. Zito, On a relation between uniform coding and problems of the form DTIME(F)=? DSPACE(F), submitted to Acta Informatica.Google Scholar
  4. 4.
    P. Clote, A time-space hierarchy between polynomial time and polynomial space, Math. Systems Theory, 25(1992) 77–92.Google Scholar
  5. 5.
    A. Cobham, The intrinsic computational complexity of functions, in Y. Bar Hillel, ed., Proc. Int. Conf. Logic, Methodology and Philosophy Sci. (North-Holland, Amsterdam, 1965) 24–30.Google Scholar
  6. 6.
    J. Hartmanis and R.E. Stearns, On the computational complexity of algorithms. Trans. A.M.S. 117(1965)285–306.Google Scholar
  7. 7.
    S.C. Kleene, Introduction to metamathematics (North-Holland, Amsterdam, 1952).Google Scholar
  8. 8.
    M. Kutylowski, A generalyzed Grzegorczyk hierarchy and low complexity classes, Information and Computation, 72.2(1987) 133–149.Google Scholar
  9. 9.
    D. Leivant, A foundational delineation of computational feasibility. 6th Annual IEEE symposium on Logic in computer science (1991).Google Scholar
  10. 10.
    D.Leivant and J.Y. Marion, Lambda calculus characterization of Poly-time (to appear on Fundamenta Informaticae).Google Scholar
  11. 11.
    M. Liskiewicz, K. Lorys, and M. Piotrow, The characterization of some complexity classes by recursion schemata, in Colloquia Mathematica Societatis János Bolyai, 44, (Pécs, 1984) 313–322.Google Scholar
  12. 12.
    Mecca and Bonner, Sequences, Datalog and transducers, PODS 1995 (reference to be revs'd in the final version of this paper).Google Scholar
  13. 13.
    C.H. Papadimitriou, A note on expressive power of PROLOG, Bull. EATCS, 26(1985) 21–23.Google Scholar
  14. 14.
    H. Poincaré Les mathématiques et la logique, Revue de Métaphisique et de Morale, 14(1906)297–317.Google Scholar
  15. 15.
    R. W. Ritchie, Classes of predictably computable functions, Trans. Am. Math. Soc. 106(1963) 139–173.Google Scholar
  16. 16.
    H.E. Rose, Subrecursion: Functions and hierarchies, (Oxford Press, Oxford, 1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Salvatore Caporaso
    • 1
  • Michele Zito
    • 2
  • Nicola Galesi
    • 3
  • Emanuele Covino
    • 4
  1. 1.Dip. di InformaticaUniv di BariItalia
  2. 2.University of Warwick CoventryUK
  3. 3.Universitat Politecnica de CatalunyaBarcelona
  4. 4.Abt. th. InformatikUniversität UlmDeutschland

Personalised recommendations