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Storage Modification Machines

In 1970 the author introduced a new machine model [A. Schonhage, Universelle Turing Speicherung, Dorr, Hotz, eds., Automatentheorie and Formale Sprachen, Bibliogr. Institut, Mannheim, 1970, pp. 369–383] now called storage modification machine (SMM). This paper gives a comprehensive presentation of our present knowledge of SMMs. It contains a complete description of the SMM model and its real time equivalence to the so-called successor RAMS. The preliminary version [A. Schonhage, Real-time simulation of multidimensional Turing machines by storage modification machines, Technical Memorandum 37, M.I.T. Project MAC, Cambridge, MA, 1973] of our proof for the real time simulation of multi-dimensional Turing machines is now worked out in its details. Moreover we show the existence of an SMM that performs integer-multiplication in linear time. The final discussion contains a brief comment on the relationship between SMMs and Kolmogorov algorithms [A. N. Kolmogorov and V. A. Uspenskii, On the definition of an algo...