Rudimentary relations and primitive recursion: A toolbox

Theoretical Computer Science

Volumn 193, Issue 1-2, 1998, Pages 129-148

  Esbelin, Henri Alex ^a   More, Malika ^b  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b UNIVERSITÉ DE CAEN   (France)

Author keywords

Coding; Counting; Primitive recursion; Rudimentary relations

Indexed keywords

EID: 0001689080     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(97)00002-9     Document Type: Article

References (29)

1. J.H. Bennett, On Spectra, Doctoral Dissertation, Princeton University, Princeton, NJ, 1962.
2. P. Cegielski, Le théorème de Dirichlet est finitiste, Preprint LITP 92.40, Université Paris 6-Paris 7, 1992.
3. C. Dimitracopoulos, Matijasevic's theorem and fragments of arithmetic, Ph. D. Thesis, University of Manchester, 1980.
4. H.A. Esbelin, Relations rudimentaires et petites classes de fonctions récursives. Doctoral Dissertation, Université d'Auvergne, 1994.
5. H.A. Esbelin, Une classe minimale de fonctions récursives contenant les relations rudimentaires, C. R. Acad. Sci. Paris, Série I, Paris, 1994, pp. 505-508.
6. H.A. Esbelin, M. More, L'ensemble des nombres de Fibonacci est rudimentaire, Preprint LLAIC1, 39, Université d'Auvergne, 1994.
7. K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I. Monatshefte für Math. Phys. 38 (1931) 173-198.
8. A. Grzegorczyk, Some Classes of Recursive Functions, Rozprawy Matematyczne 4 (1953) 1-46.
9. K. Harrow, Sub-elementary classes of functions and relations, Doctoral Dissertation, New York University, Department of Mathematics, 1973.
10. K. Harrow, Small Grzegorczyk classes and limited minimum, Z. Math. Logik Grundlagen Math. 11 (1975) 417-426.
11. N.D. Jones, Context-free languages and rudimentary attributes, Math. System Theory 3 (1969) 102-109.
12. R.M. Karp, Reducibility among combinatorial problems, IBM Symp. 1972, Complexity of Computers Computations, Plenum Press, New York, 1972.
13. M. Kutylovski, Small Grzegorczyk classes, J. London Math. Soc. 2 (36) (1987) 193-210.
14. J. Malifaud, Contribution à l'étude des fonctions calculables de croissance limitéé, Doctoral Dissertation, Université Paris 7, 1985.
15. J. Meloul, Rudimentary predicates, low complexity classes and related automata, Ph.D. Dissertation, Oxford University, 1979.
16. M. More, Rudimentary representations of spectra, Prépublication du LLAICl, Numéro 40, 1994.
17. M. More, F. Olive, Rudimentary languages and second-order logic, Préprint GRAL, 1996-1, 1996.
18. G. Myhill, Linear bounded automata, Wright Air Devel. Div., Tech. Note 60-165, Wright-Patterson Air Force Base, OH, 1960.
19. 0 sets, Fund. Math. 127 (1987).
20. W. Quine, Concatenation as a basis for arithmetic from a logical point of view, J. Symbol. Logic 11 (1946) 105-114. Selected Logic Papers, Random House, 1966, ch. V, pp. 70-82.
21. W. Quine, Concatenation as a basis for arithmetic from a logical point of view, J. Symbol. Logic 11 (1946) 105-114. Selected Logic Papers, Random House, 1966, ch. V, pp. 70-82.
22. R.W. Ritchie, Classes of Predictably Computable Functions, Trans. Amer. Math. Soc. 106 (1963) 139-173.
23. H.Jr. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967.
24. H. Shapiro, Introduction to the Theory of numbers, Wiley, New York, 1982.
25. R. Smullyan, Theory of Formal Systems, Ann. Math. Studies, vol. 47, Princeton University Press, Princeton, NJ, 1961.
26. L.J. Stockmeyer, The polynomial time hierarchy, Theor. Comput. Sci. 3 (1976) 1-22.
27. A. Woods, Some problems in logic and number theory, and their connections, Doctoral Dissertation, University of Manchester, 1981.
28. C. Wrathall, Rudimentary predicates and relative computation, SIAM J Comput. 7(2) (1978) 194-209.
29. C. Calude, Super-exponential non primitive recursive, but rudimentary, Information Processing Letters 25 (1987) 311-315.