@MISC{Rose96characterizingcomputation, author = {Eva Rose}, title = {Characterizing Computation Models with a Constant Factor Time Hierachy}, year = {1996} }

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Abstract

The existence of a constant factor time hierarchy within sets decidable within a (time-constructible) time bound is a necessary property for reasoning theoretically about linear time optimizations. However, proving this property typically involves careful construction of custom interpreters or compilers, which is a tedious affair. A more generic method to state the existence or not is desirable. In this note, we discuss some aspects of finite branching for a programming language (viewed as a computation model) which are necessary for the existence of a time-hierarchy assuming a realistic memory organization and implementation: a finite number of constructors, variables, and functions, and finite branching of data and control. Then, we analyse some languages for which the existence of a constant factor time-hierarchy is already known. Finally, we draw the analogy to traditional machine model theory. 1 Background We assume the reader to be familiar with the idea of complexity from a pro...