Ackermann function (English Wikipedia)

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

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20doi.org

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2jstor.org

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2arxiv.org

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ams.org

mathscinet.ams.org

Wiernik & Sharir 1988. Wiernik, Ady; Sharir, Micha (1988). "Planar realizations of nonlinear Davenport–Schinzel sequences by segments". Discrete & Computational Geometry. 3 (1): 15–47. doi:10.1007/BF02187894. MR 0918177.

arxiv.org

Czerwiński & Orlikowski 2022. Czerwiński, Wojciech; Orlikowski, Łukasz (7 February 2022). Reachability in Vector Addition Systems is Ackermann-complete. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.13866. doi:10.1109/FOCS52979.2021.00120.
Leroux 2022. Leroux, Jérôme (7 February 2022). The Reachability Problem for Petri Nets is Not Primitive Recursive. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.12695. doi:10.1109/FOCS52979.2021.00121.

books.google.com

Monin & Hinchey 2003, p. 61. Monin, Jean-Francois; Hinchey, M. G. (2003). Understanding Formal Methods. Springer. p. 61. ISBN 9781852332471.

doi.org

The maximum depth of recursion refers to the number of levels of activation of a procedure which exist during the deepest call of the procedure. Cornelius & Kirby (1975) Cornelius, B.J.; Kirby, G.H. (1975). "Depth of recursion and the ackermann function". BIT Numerical Mathematics. 15 (2): 144–150. doi:10.1007/BF01932687. S2CID 120532578.
Ackermann 1928. Ackermann, Wilhelm (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen. 99: 118–133. doi:10.1007/BF01459088. S2CID 123431274.
Calude, Marcus & Tevy 1979. Calude, Cristian; Marcus, Solomon; Tevy, Ionel (November 1979). "The first example of a recursive function which is not primitive recursive". Historia Math. 6 (4): 380–84. doi:10.1016/0315-0860(79)90024-7.
Hilbert 1926, p. 185. Hilbert, David (1926). "Über das Unendliche". Mathematische Annalen. 95: 161–190. doi:10.1007/BF01206605. S2CID 121888793.
Péter 1935. Péter, Rózsa (1935). "Konstruktion nichtrekursiver Funktionen". Mathematische Annalen. 111: 42–60. doi:10.1007/BF01472200. S2CID 121107217.
Robinson 1948. Robinson, Raphael Mitchel (1948). "Recursion and Double Recursion". Bulletin of the American Mathematical Society. 54 (10): 987–93. doi:10.1090/S0002-9904-1948-09121-2.
Ritchie 1965, p. 1028. Ritchie, Robert Wells (November 1965). "Classes of recursive functions based on Ackermann's function". Pacific Journal of Mathematics. 15 (3): 1027–1044. doi:10.2140/pjm.1965.15.1027.
Buck 1963. Buck, R.C. (1963). "Mathematical Induction and Recursive Definitions". American Mathematical Monthly. 70 (2): 128–135. doi:10.2307/2312881. JSTOR 2312881.
Ritchie 1965. Ritchie, Robert Wells (November 1965). "Classes of recursive functions based on Ackermann's function". Pacific Journal of Mathematics. 15 (3): 1027–1044. doi:10.2140/pjm.1965.15.1027.
Sundblad 1971. Sundblad, Yngve (March 1971). "The Ackermann function. A theoretical, computational, and formula manipulative study". BIT Numerical Mathematics. 11 (1): 107–119. doi:10.1007/BF01935330. S2CID 123416408.
Porto & Matos 1980. Porto, António; Matos, Armando B. (1 September 1980). "Ackermann and the superpowers" (PDF). ACM SIGACT News. 12 (3): Original version 1980, published in “ACM SIGACT News”, Modified in October 20, 2012, Modified in January 23, 2016 (working paper). doi:10.1145/1008861.1008872. S2CID 29780652. Archived (PDF) from the original on 9 October 2022.
Grossman & Zeitman 1988. Grossman, Jerrold W.; Zeitman, R.Suzanne (May 1988). "An inherently iterative computation of ackermann's function". Theoretical Computer Science. 57 (2–3): 327–330. doi:10.1016/0304-3975(88)90046-1.
Pettie 2002. Pettie, S. (2002). "An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem". The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. pp. 155–163. doi:10.1109/SFCS.2002.1181892. ISBN 0-7695-1822-2. S2CID 8636108.
Czerwiński & Orlikowski 2022. Czerwiński, Wojciech; Orlikowski, Łukasz (7 February 2022). Reachability in Vector Addition Systems is Ackermann-complete. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.13866. doi:10.1109/FOCS52979.2021.00120.
Leroux 2022. Leroux, Jérôme (7 February 2022). The Reachability Problem for Petri Nets is Not Primitive Recursive. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.12695. doi:10.1109/FOCS52979.2021.00121.
Tarjan 1975. Tarjan, Robert Endre (1975). "Efficiency of a Good But Not Linear Set Union Algorithm". Journal of the ACM. 22 (2): 215–225. doi:10.1145/321879.321884. hdl:1813/5942. S2CID 11105749.
Fredman & Saks 1989. Fredman, M.; Saks, M. (May 1989). "The cell probe complexity of dynamic data structures". Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89. pp. 345–354. doi:10.1145/73007.73040. ISBN 0897913078. S2CID 13470414.
Wiernik & Sharir 1988. Wiernik, Ady; Sharir, Micha (1988). "Planar realizations of nonlinear Davenport–Schinzel sequences by segments". Discrete & Computational Geometry. 3 (1): 15–47. doi:10.1007/BF02187894. MR 0918177.
Wichmann 1976. Wichmann, Brian A. (March 1976). "Ackermann's function: A study in the efficiency of calling procedures". BIT Numerical Mathematics. 16: 103–110. CiteSeerX 10.1.1.108.4125. doi:10.1007/BF01940783. S2CID 16993343.
Wichmann 1977. Wichmann, Brian A. (July 1977). "How to call procedures, or second thoughts on Ackermann's function". BIT Numerical Mathematics. 16 (3): 103–110. doi:10.1002/spe.4380070303. S2CID 206507320.

ed.ac.uk

history.dcs.ed.ac.uk

Wichmann 1982. Wichmann, Brian A. (July 1982). "Latest results from the procedure calling test, Ackermann's function" (PDF). Archived (PDF) from the original on 9 October 2022.

ghostarchive.org

Meeussen & Zantema 1992, p. 6. Meeussen, V.C.S.; Zantema, H. (1992). Derivation lengths in term rewriting from interpretations in the naturals (PDF) (Report). Universiteit Utrecht. UU-CS, Department of Computer Science. ISSN 0924-3275. Archived (PDF) from the original on 9 October 2022.
Porto & Matos 1980. Porto, António; Matos, Armando B. (1 September 1980). "Ackermann and the superpowers" (PDF). ACM SIGACT News. 12 (3): Original version 1980, published in “ACM SIGACT News”, Modified in October 20, 2012, Modified in January 23, 2016 (working paper). doi:10.1145/1008861.1008872. S2CID 29780652. Archived (PDF) from the original on 9 October 2022.
Matos 2014. Matos, Armando B (7 May 2014). "The inverse of the Ackermann function is primitive recursive" (PDF). Archived (PDF) from the original on 9 October 2022.
Wichmann 1982. Wichmann, Brian A. (July 1982). "Latest results from the procedure calling test, Ackermann's function" (PDF). Archived (PDF) from the original on 9 October 2022.

handle.net

hdl.handle.net

Tarjan 1975. Tarjan, Robert Endre (1975). "Efficiency of a Good But Not Linear Set Union Algorithm". Journal of the ACM. 22 (2): 215–225. doi:10.1145/321879.321884. hdl:1813/5942. S2CID 11105749.

ieee.org

ieeexplore.ieee.org

Czerwiński & Orlikowski 2022. Czerwiński, Wojciech; Orlikowski, Łukasz (7 February 2022). Reachability in Vector Addition Systems is Ackermann-complete. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.13866. doi:10.1109/FOCS52979.2021.00120.
Leroux 2022. Leroux, Jérôme (7 February 2022). The Reachability Problem for Petri Nets is Not Primitive Recursive. Proceedings of the 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science. arXiv:2104.12695. doi:10.1109/FOCS52979.2021.00121.

jstor.org

Buck 1963. Buck, R.C. (1963). "Mathematical Induction and Recursive Definitions". American Mathematical Monthly. 70 (2): 128–135. doi:10.2307/2312881. JSTOR 2312881.
Vaida 1970. Vaida, Dragoș (1970). "Compiler Validation for an Algol-like Language". Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle série. 14 (62) (4): 487–502. JSTOR 43679758.

kosara.net

"Decimal expansion of A(4,2)". kosara.net. 27 August 2000. Archived from the original on 20 January 2010.

mrob.com

Munafo 1999a. Munafo, Robert (1999a). "Versions of Ackermann's Function". Large Numbers at MROB. Retrieved 6 November 2021.

msp.org

Ritchie 1965, p. 1028. Ritchie, Robert Wells (November 1965). "Classes of recursive functions based on Ackermann's function". Pacific Journal of Mathematics. 15 (3): 1027–1044. doi:10.2140/pjm.1965.15.1027.
Ritchie 1965. Ritchie, Robert Wells (November 1965). "Classes of recursive functions based on Ackermann's function". Pacific Journal of Mathematics. 15 (3): 1027–1044. doi:10.2140/pjm.1965.15.1027.

projecteuclid.org

Robinson 1948. Robinson, Raphael Mitchel (1948). "Recursion and Double Recursion". Bulletin of the American Mathematical Society. 54 (10): 987–93. doi:10.1090/S0002-9904-1948-09121-2.

psu.edu

citeseerx.ist.psu.edu

Wichmann 1976. Wichmann, Brian A. (March 1976). "Ackermann's function: A study in the efficiency of calling procedures". BIT Numerical Mathematics. 16: 103–110. CiteSeerX 10.1.1.108.4125. doi:10.1007/BF01940783. S2CID 16993343.

quantamagazine.org

Brubaker 2023. Brubaker, Ben (4 December 2023). "An Easy-Sounding Problem Yields Numbers Too Big for Our Universe".

researchgate.net

Paulson 2021. Paulson, Lawrence C. (2021). "Ackermann's Function in Iterative Form: A Proof Assistant Experiment". Retrieved 19 October 2021.

semanticscholar.org

api.semanticscholar.org

The maximum depth of recursion refers to the number of levels of activation of a procedure which exist during the deepest call of the procedure. Cornelius & Kirby (1975) Cornelius, B.J.; Kirby, G.H. (1975). "Depth of recursion and the ackermann function". BIT Numerical Mathematics. 15 (2): 144–150. doi:10.1007/BF01932687. S2CID 120532578.
Ackermann 1928. Ackermann, Wilhelm (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen. 99: 118–133. doi:10.1007/BF01459088. S2CID 123431274.
Hilbert 1926, p. 185. Hilbert, David (1926). "Über das Unendliche". Mathematische Annalen. 95: 161–190. doi:10.1007/BF01206605. S2CID 121888793.
Péter 1935. Péter, Rózsa (1935). "Konstruktion nichtrekursiver Funktionen". Mathematische Annalen. 111: 42–60. doi:10.1007/BF01472200. S2CID 121107217.
Sundblad 1971. Sundblad, Yngve (March 1971). "The Ackermann function. A theoretical, computational, and formula manipulative study". BIT Numerical Mathematics. 11 (1): 107–119. doi:10.1007/BF01935330. S2CID 123416408.
Porto & Matos 1980. Porto, António; Matos, Armando B. (1 September 1980). "Ackermann and the superpowers" (PDF). ACM SIGACT News. 12 (3): Original version 1980, published in “ACM SIGACT News”, Modified in October 20, 2012, Modified in January 23, 2016 (working paper). doi:10.1145/1008861.1008872. S2CID 29780652. Archived (PDF) from the original on 9 October 2022.
Pettie 2002. Pettie, S. (2002). "An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem". The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. pp. 155–163. doi:10.1109/SFCS.2002.1181892. ISBN 0-7695-1822-2. S2CID 8636108.
Tarjan 1975. Tarjan, Robert Endre (1975). "Efficiency of a Good But Not Linear Set Union Algorithm". Journal of the ACM. 22 (2): 215–225. doi:10.1145/321879.321884. hdl:1813/5942. S2CID 11105749.
Fredman & Saks 1989. Fredman, M.; Saks, M. (May 1989). "The cell probe complexity of dynamic data structures". Proceedings of the twenty-first annual ACM symposium on Theory of computing - STOC '89. pp. 345–354. doi:10.1145/73007.73040. ISBN 0897913078. S2CID 13470414.
Wichmann 1976. Wichmann, Brian A. (March 1976). "Ackermann's function: A study in the efficiency of calling procedures". BIT Numerical Mathematics. 16: 103–110. CiteSeerX 10.1.1.108.4125. doi:10.1007/BF01940783. S2CID 16993343.
Wichmann 1977. Wichmann, Brian A. (July 1977). "How to call procedures, or second thoughts on Ackermann's function". BIT Numerical Mathematics. 16 (3): 103–110. doi:10.1002/spe.4380070303. S2CID 206507320.

tue.nl

research.tue.nl

Meeussen & Zantema 1992, p. 6. Meeussen, V.C.S.; Zantema, H. (1992). Derivation lengths in term rewriting from interpretations in the naturals (PDF) (Report). Universiteit Utrecht. UU-CS, Department of Computer Science. ISSN 0924-3275. Archived (PDF) from the original on 9 October 2022.

uni-goettingen.de

gdz.sub.uni-goettingen.de

Ackermann 1928. Ackermann, Wilhelm (1928). "Zum Hilbertschen Aufbau der reellen Zahlen". Mathematische Annalen. 99: 118–133. doi:10.1007/BF01459088. S2CID 123431274.

up.pt

dcc.fc.up.pt

Porto & Matos 1980. Porto, António; Matos, Armando B. (1 September 1980). "Ackermann and the superpowers" (PDF). ACM SIGACT News. 12 (3): Original version 1980, published in “ACM SIGACT News”, Modified in October 20, 2012, Modified in January 23, 2016 (working paper). doi:10.1145/1008861.1008872. S2CID 29780652. Archived (PDF) from the original on 9 October 2022.
Matos 2014. Matos, Armando B (7 May 2014). "The inverse of the Ackermann function is primitive recursive" (PDF). Archived (PDF) from the original on 9 October 2022.

web.archive.org

"Decimal expansion of A(4,2)". kosara.net. 27 August 2000. Archived from the original on 20 January 2010.

worldcat.org

search.worldcat.org

Meeussen & Zantema 1992, p. 6. Meeussen, V.C.S.; Zantema, H. (1992). Derivation lengths in term rewriting from interpretations in the naturals (PDF) (Report). Universiteit Utrecht. UU-CS, Department of Computer Science. ISSN 0924-3275. Archived (PDF) from the original on 9 October 2022.