Ranking primitive recursions: The low Grzegorczyk classes revisited

SIAM Journal on Computing

Volumn 29, Issue 2, 1999, Pages 401-415

  Bellantoni, Stephen J ^a   Niggl, Karl Heinz ^b  

^a Fak Informatik und Automatisierung ^*  (Canada)

^b ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; POLYNOMIALS; THEOREM PROVING;

GRZEGORCZYK HIERARCHY; PRIMITIVE RECURSIVE FUNCTIONS; SCHWICHTENBERG-MULLER THEOREMS;

RECURSIVE FUNCTIONS;

EID: 0033301161     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S009753979528175X     Document Type: Article

References (23)

1. S. BELLANTONI, Ranking arithmetic proofs by implicit ramification, in Proof of Complexity and Feasible Arithmetics, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 39, AMS, Providence, RI, 1998, pp. 37-57.
2. S. BELLANTONI, Predicative recursion and the polytime hierarchy, in Feasible Mathematics II, P. Clote and J. B. Remmel eds., Birkhäuser, Boston, 1995, pp. 15-29.
3. S. BELLANTONI, Predicative Recursion and Computational Complexity, Tech. report 264/92, Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, 1992.
4. S. BELLANTONI AND S. COOK, A new recursion-theoretic characterization of the polytime functions, Comput. Complexity, 2 (1992), pp. 97-110.
5. S. BLOCH, Function-algebraic characterizations of log and polylog parallel time, Comput. Complexity, 4 (1994), pp. 175-205.
6. P. CLOTE, Computation models and function algebras, in Handbook of Recursion Theory, Ed Griffor, ed., Elsevier, New York, 1996, pp. 1-90.
7. A. COBHAM, The intrinsic computational difficulty of functions. 1965 Logic, Methodology and Philos. Sci., Proc. 1964 Internat. Cong., Y. Bar-Hillel, ed., North-Holland, Amsterdam, 1965.
8. A. GRZEGORCZYK, Some classes of recursive functions, Rozprawy Mat., 4 (1953).
9. W. G. HANDLEY, Bellantoni and Cook's Characterization of Polynomial Time Functions, manuscript, August 1992.
10. D. LEIVANT, Intrinsic theories and computational complexity, Lecture Notes in Comput. Sci. 960, Springer-Verlag, New York, 1995, pp. 177-194.
11. D. LEIVANT, Ramified recurrence and computational complexity I: Word recurrence and polytime, in Feasible Mathematics II, P. Clote and J. B. Remmel eds., Birkhäuser, Boston, 1995, pp. 321-343.
12. D. LEIVANT, Stratified functional programs and computational complexity, in Conference Record of the Twentieth Annual ACM Symposium on Principles of Programming Languages, New York, 1993, ACM, New York, pp.
13. D. LEIVANT, AND J.-Y. MARION, Ramified recurrence and computational complexity II: Substitution and poly-space, in Computer Science Logic, J. Tiuryn and L. Pacholsky, eds., Lecture Notes in Comput. Sci. 933, Springer-Verlag, Berlin. 1995, pp. 486-500.
14. D. LEIVANT, Ramified recurrence and computational complexity III: Higher-type recurrence and elementary complexity, in Annals of Pure and Applied Logic 96, M. Fitting, R. Ramanujam, and K. Georgatos, eds., 1999, p. 209.
15. H. MÜLLER, Klassifizierungen der primitiv rekursiven Funktionen, Ph.D. thesis, Universität Münster, 1974.
16. w-terms, Ann. Pure Appl. Logic, 75 (1995), pp. 153-178.
17. K.-H. NIGGL, The μ-Measure as a Tool for Classifying Computational Complexity, http: www.eiche.theoinf.tu-ilmenau.de/ niggl; to appear in Archive for Mathematical Logic.
18. A. NGUYEN, A Formal System For Linear-Space Reasoning, Tech. report 330/96, Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, 1993.
19. I. OITAVEM, New recursive characterizations of the elementary functions and the functions computable in polynomial space, Rev. Mat. Univ. Complut Madrid, 10 (1997), pp. 109-125.
20. C. PARSONS, Hierarchies of primitive recursive functions, Z. Math. Logik Grundlagen Math., 14 (1968), pp. 357-376.
21. G. PLOTKIN, LCF considered as a programming language, Theoret. Comput. Sci., 5 (1977), pp. 223-255.
22. R. W. RITCHIE, Classes of predictably computable functions, Trans. Amer. Math. Soc., 106 (1963), pp. 139-173.
23. H. SCHWICHTENBERG, Rekursionszahlen und die Grzegorczyk-Hierarchie, Arch. Math. Logik, Grundlagen forsch., 12 (1969), pp. 85-96.