Primitive recursive function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Primitive recursive function" in English language version.

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Hartmanis 1989. Hartmanis, Juris (1989), "Overview of Computational Complexity Theory", Computational Complexity Theory, Proceedings of Symposia in Applied Mathematics, vol. 38, American Mathematical Society, pp. 1–17, ISBN 978-0-8218-0131-4, MR 1020807
Robinson 1947. Robinson, Raphael M. (1947), "Primitive recursive functions", Bulletin of the American Mathematical Society, 53 (10): 925–942, doi:10.1090/S0002-9904-1947-08911-4, MR 0022536
Gladstone 1967. Gladstone, M. D. (1967), "A reduction of the recursion scheme", The Journal of Symbolic Logic, 32 (4): 505–508, doi:10.2307/2270177, JSTOR 2270177, MR 0224460
Gladstone 1971. Gladstone, M. D. (1971), "Simplifications of the recursion scheme", The Journal of Symbolic Logic, 36 (4): 653–665, doi:10.2307/2272468, JSTOR 2272468, MR 0305993
Severin 2008. Severin, Daniel E. (2008), "Unary primitive recursive functions", The Journal of Symbolic Logic, 73 (4): 1122–1138, arXiv:cs/0603063, doi:10.2178/jsl/1230396909, JSTOR 275903221, MR 2467207

Severin 2008. Severin, Daniel E. (2008), "Unary primitive recursive functions", The Journal of Symbolic Logic, 73 (4): 1122–1138, arXiv:cs/0603063, doi:10.2178/jsl/1230396909, JSTOR 275903221, MR 2467207

This follows from the facts that the functions of this form are the most quickly growing primitive recursive functions, and that a function is primitive recursive if and only if its time complexity is bounded by a primitive recursive function. For the former, see Linz, Peter (2011), An Introduction to Formal Languages and Automata, Jones & Bartlett Publishers, p. 332, ISBN 9781449615529. For the latter, see Moore, Cristopher; Mertens, Stephan (2011), The Nature of Computation, Oxford University Press, p. 287, ISBN 9780191620805

Robinson 1947. Robinson, Raphael M. (1947), "Primitive recursive functions", Bulletin of the American Mathematical Society, 53 (10): 925–942, doi:10.1090/S0002-9904-1947-08911-4, MR 0022536
Gladstone 1967. Gladstone, M. D. (1967), "A reduction of the recursion scheme", The Journal of Symbolic Logic, 32 (4): 505–508, doi:10.2307/2270177, JSTOR 2270177, MR 0224460
Gladstone 1971. Gladstone, M. D. (1971), "Simplifications of the recursion scheme", The Journal of Symbolic Logic, 36 (4): 653–665, doi:10.2307/2272468, JSTOR 2272468, MR 0305993
Severin 2008. Severin, Daniel E. (2008), "Unary primitive recursive functions", The Journal of Symbolic Logic, 73 (4): 1122–1138, arXiv:cs/0603063, doi:10.2178/jsl/1230396909, JSTOR 275903221, MR 2467207
Meyer, Albert R.; Ritchie, Dennis M. (1967), "The complexity of loop programs", ACM '67: Proceedings of the 1967 22nd national conference, pp. 465–469, doi:10.1145/800196.806014

Gladstone 1967. Gladstone, M. D. (1967), "A reduction of the recursion scheme", The Journal of Symbolic Logic, 32 (4): 505–508, doi:10.2307/2270177, JSTOR 2270177, MR 0224460
Gladstone 1971. Gladstone, M. D. (1971), "Simplifications of the recursion scheme", The Journal of Symbolic Logic, 36 (4): 653–665, doi:10.2307/2272468, JSTOR 2272468, MR 0305993
Severin 2008. Severin, Daniel E. (2008), "Unary primitive recursive functions", The Journal of Symbolic Logic, 73 (4): 1122–1138, arXiv:cs/0603063, doi:10.2178/jsl/1230396909, JSTOR 275903221, MR 2467207

Peter Smith (2013), An Introduction to Gödel's Theorems (2nd ed.), Cambridge University Press, pp. 98–99, ISBN 978-1-107-02284-3

Kleene 1974, pp. 226–227. Kleene, Stephen Cole (1974) [1952], "Chapter XI. General Recursive Functions §57", Introduction to Metamathematics (7th reprint; 2nd ed.), North-Holland Publishing Company, ISBN 0444100881, OCLC 3757798