Abstract
A RAM program is said to run within a “strong” time bound T if on every sequence of n inputs it terminates within T( n) instruction executions. There are some programs whose execution time in this sense is a non-computable function of n. It is shown that such programs are essential in the sense that some functions can be computed within a non-computable time bound but not within any computable time bound. Nevertheless, strong time bounds are subject to a powerful hierarchy theorem. The condition such as being time constructable which normally applies to the “lower” function in such theorems is replaced by a condition of being the minimum strong time bound for some program.
Published Version
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