Abstract
This survey paper presents a complexity theoretical approach to genuinely time bounded computations. Such computations are executed by random access machines with given set \(S \subseteq \{ + , - ,*,DIV,...\}\)of arithmetic operations. The uniform cost measure is assumed, and the input is given integer by integer, not bit by bit. “Genuinely” (also called “strongly” in the literature) means that we measure the time complexity T(n) as the worst case runtime over all inputs consisting of n integers (not of n bits). Computability and complexity now heavily depend on the operation set S. In this paper genuine complexity classes for given operation sets S are defined, following ideas due to Karpinski and the author from [KaM 88]. Furthermore, results on genuine computability, lower bound methods, as well as examples for complexity gaps and separated complexity classes are surveyed.
Supported in part by DFG-Grants ME 872/1-2 and WE 1066/2-1
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© 1989 Springer-Verlag Berlin Heidelberg
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Meyer auf der Heide, F. (1989). On genuinely time bounded computations. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028969
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DOI: https://doi.org/10.1007/BFb0028969
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