Abstract
In usual computers - that use binary representation of real numbers - an irrational real number (and even a rational number like 1.3 or 1.2) can only be computed with a finite accuracy. The more accuracy we need, the larger the computation time. It is therefore reasonable to characterize the complexity of computing a real number a by the accuracy Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> (t) that we can achieve in time t. Once we know this characteristic for two numbers a and b, how can we compute a similar characteristic for, e.g., c = a + b? In this paper, we show that the problem of computing this characteristic can be reduced to the problem of computing the membership function for the sum - when we use Zadeh's extension principle with algebraic product as the “and”-operation. Thus, known algorithms for computing this membership function can be used to describe computations under time constraints.
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