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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Complexity Vol. 14; no. 4; pp. 490 - 526
Main Authors: Brattka, Vasco, Hertling, Peter
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.1998
Subjects:
complexity in analysis
computability
computational complexity
computability
complexity in analysis
computational complexity
ISSN:0885-064X, 1090-2708
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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