Turing's Universal Machine
Appendix Turing’s Universal Machine This appendix gives the complete table for the universal Turing machine U. There were a number of errors in Turing’s original paper, as pointed out by Emil Post and Donald Davies.1 These errors have been corrected in the tables below. A.1 General Purpose m-functions The tape of the universal machine uses the convention of alternating F-squares and E-squares, described in Sect. 4.5, where the E-squares are used to mark, or label, symbols on the preceding F-squares. The leftmost point of the portion of the tape used in the computation is identified by means of the symbol e placed in a pair of adjacent squares. f(C, B,α): find The m-function f(C, B,α) finds the leftmost occurrence on the tape of the symbol α, and then moves to m-configuration C. If there is no occurrence of α on the tape, the machine moves to m-configuration B. m-config. symbol operations final m-config. e L f1(C, B,α) f(C, B,α) e not L f(C, B,α) ⎧ ⎨ α C f1(C, B,α) ⎩ not αR f1(C, B,α) None R f (C, B,α) ⎧ 2 ⎨ α C f2(C, B,α) ⎩ not αR f1(C, B,α) None R B 1See Post (1947) and Davies (2004). Davies describes Turing’s “impatience” when these errors were pointed out, remembering that he “made it clear that I was wasting my time and his by my worthless endeavors”. M. Priestley, A Science of Operations, History of Computing, 307 DOI 10.1007/978-1-84882-555-0, © Springer-Verlag London Limited 2011 308 Turing’s Universal Machine e(C, B,α): erase The m-function e(C, B,α)erases the leftmost occurrence on the tape of the symbol α, and then moves to m-configuration C.
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