A new hierarchy of elementary functions
HTML articles powered by AMS MathViewer
- by G. T. Herman
- Proc. Amer. Math. Soc. 20 (1969), 557-562
- DOI: https://doi.org/10.1090/S0002-9939-1969-0250878-2
- PDF | Request permission
References
- Paul Axt, Enumeration and the Grzegorczyk hierarchy, Z. Math. Logik Grundlagen Math. 9 (1963), 53–65. MR 144811, DOI 10.1002/malq.19630090106
- J. P. Cleave, A hierarchy of primitive recursive functions, Z. Math. Logik Grundlagen Math. 9 (1963), 331–346. MR 159754, DOI 10.1002/malq.19630092202
- Patrick C. Fischer, On formalisms for Turing machines, J. Assoc. Comput. Mach. 12 (1965), 570–580. MR 191826, DOI 10.1145/321296.321308
- Andrzej Grzegorczyk, Some classes of recursive functions, Rozprawy Mat. 4 (1953), 46. MR 60426 G. T. Herman, Turing machines and their applications to Hilbert’s tenth problem, M.Sc. Thesis, University of London, 1964. —, A definition of simulation for discrete computing systems, Third Internat. Congr. for Logic, Methodology and Philosophy of Science, Amsterdam, 1967. —, On hierarchies of elementary functions, Proc. Internat. Colloq. Recursive Functions and their Applications (Tihany, 1967), Institut Blaise Pascal, Paris and Bolyai Janos Matematikai Tarsulat, Budapest, (in press).
- Robert W. Ritchie, Classes of predictably computable functions, Trans. Amer. Math. Soc. 106 (1963), 139–173. MR 158822, DOI 10.1090/S0002-9947-1963-0158822-2
- Claude E. Shannon, A universal Turing machine with two internal states, Automata studies, Annals of Mathematics Studies, no. 34, Princeton University Press, Princeton, N.J., 1956, pp. 157–165. MR 0079548
- J. C. Shepherdson and H. E. Sturgis, Computability of recursive functions, J. Assoc. Comput. Mach. 10 (1963), 217–255. MR 151374, DOI 10.1145/321160.321170
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 20 (1969), 557-562
- MSC: Primary 02.77
- DOI: https://doi.org/10.1090/S0002-9939-1969-0250878-2
- MathSciNet review: 0250878