Feasible Real Random Access Machines

We present a modified real RAM model which is equipped with the usual discrete and real-valued arithmetic operations and with a finite precision test <kwhich allows comparisons of real numbers only up to a variable uncertainty 1/(k+1). Furthermore, ourfeasible RAMhas an extended semantics which a...

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Vydáno v:Journal of Complexity Ročník 14; číslo 4; s. 490 - 526
Hlavní autoři: Brattka, Vasco, Hertling, Peter
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.12.1998
Témata:
complexity in analysis
computability
computational complexity
computability
complexity in analysis
computational complexity
ISSN:0885-064X, 1090-2708
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Shrnutí:We present a modified real RAM model which is equipped with the usual discrete and real-valued arithmetic operations and with a finite precision test <kwhich allows comparisons of real numbers only up to a variable uncertainty 1/(k+1). Furthermore, ourfeasible RAMhas an extended semantics which allows approximative computations. Using a logarithmic complexity measure we prove that all functions computable on a RAM in time O(t) can be computed on a Turing machine in time O(t2·log(t)·loglog(t)). Vice versa all functions computable on a Turing machine in time O(t) are computable on a RAM in time O(t). Thus, our real RAM model does not only express exactly the computational power of Turing machines on real numbers (in the sense of Grzegorczyk), but it also yields a high-level tool for realistic time complexity estimations on real numbers.
ISSN:0885-064X
1090-2708
DOI:10.1006/jcom.1998.0488