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FRACTRAN: a simple universal programming language for arithmetic. (English) Zbl 1216.68068
Lagarias, Jeffrey C. (ed.), The ultimate challenge. The $3x+1$ problem. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4940-8/hbk). 249-264 (2010).
From the preface by J. Lagarias: This 1987 paper of Conway [in: Open Problems in Communication and Computation (T. M. Cover and B. Gopinath, eds.), Springer-Verlag: New York, 3--27 (1987; Zbl 0628.68001)] expands on his 1972 paper to show how to encode any computational problem in terms of iteration of a suitable $3x+1$-like function. The programming language name FRACTRAN is a pun on FORTRAN (The IBM Mathematical Formula Translating System). This is not the only pun in this paper. For the entire collection see [Zbl 1253.11003].
68N15Programming languages
11B83Special sequences of integers and polynomials
68Q05Models of computation (Turing machines, etc.)