Abstract
There is given one machine-independent description for a large number of classes of functions, computable on Turing machines with bounded memory and time. Let S and T be classes of nondecreasing functions, satisfying certain simple conditions. It is proved that the class of functions computable on Turing machines with memory bounded by a function from S in time bounded by a function from T coincides with the class of functions obtained from certain simple initial functions by means of explicit transformations, composition, and recursion of the form where s $$\varepsilon $$ S, t $$\varepsilon $$ T, ¦x¦ is the length of the binary representation of the number x. We also get analogous descriptions of classes of functions computable with bounded memory and classes of functions computable with bounded time.
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