One of the first and simplest models of a quantum computer was introduced by Richard Feynman (1985). The aim of our study is to extend the application area of Petri nets, which have been very successfully used to model classical engineering systems, by modeling the use and operation of Feynman's quantum computer. Originally, Feynman could not give a time bound for the completion of his computer's computation; a periodical measurement procedure was needed giving rise to a specific computational approach. We have chosen Feynman's NOT-computer, in the form of two /spl radic/NOT gates in series, as our object of demonstration; its use and operation are modeled in detail using stochastic high level Petri net formalism.

Recently, Silverston1has given an algorithm to produce sinusoids with only two multiplications per cycle. With a simple substitution the algorithm can be further changed to have only one multiplication per cycle. The stability of these recursive algorithms depends on the roundoff errors and it cannot be stated straightforward.

In this correspondence a class of algorithms for recursive estimation of the mean of a random yariable is described and its properties are studied. New algorithms are presented that are shown to be statisticaily more efficient than the previous algorithms, and only slightly less efficient than the optimal algorithm of the same type. The computation time remains the same as in the best previous algorithm, whereas the optimal algorithm implies a considerably longer computation time.

In this paper mathematical models for digital integrators operating with multidigit increments are given, and the discretization error analysis of their linear connections is studied. The integration methods considered are linear multistep integration methods; some examples are studied in detail. Linear digital differential analyzer (DDA) connections are defined, and their use in connection with the numerical solution of the initial value problem is explained. Finally, the discretization error in these linear DDA connections has been analyzed in detail; the theoretical results have also been verified experimentally.