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applicatin of the recursive function theory to problems of computational quantity

递归函数理论在计算量问题中的应用

基本信息

批准号：
09640257
负责人：
SATOH Junya
金额：
$ 1.92万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640257/
关键词：
recursive function computational quantity polynomial-time

项目摘要

(1)We extend a well-known formula for sums of products of two Bernoulli numbers to that of Garlitz's q-Bernoulli numbers.(2)We give a Kaneko's type of recurrence formula for the q-Bernoulli numbers attached to formal group.(3)A linearized implicit finite difference method for the KdV is proposed and straightforwardly extended to the KP equation. We investigate the order of accuracy of the method and prove the method to be unconditionally lineary stable.(4)Thehalt scheme for quantum Turing machine, originally proposed by Deutsch, is reformulated precisely and is proven to work without spoiling the computation.(5)We consider continuous-time Gaussian channels with feedback and investigate problems on the mutual information and the channel capacity. While, in most of the previous works, some conditions are imposed on the Gaussian noise, in this paper we do not require any special conditions on the Gaussian noise. We derive a formula for the mutual information transmitted over the Gaussian channel with feedback. Then we show that the capacity of the channel is achieved in linear schemes, more precisely, achieved by sending a Gaussian message with the aid of linear feedback. We also show some inequalities concerning the capacity of the channel.(6)We present a simple condition for an ideal to be nowhere precipitous. Through this condition we show nowhere precipitousness of fundamental ideals on P_<kappa>lambda paticular the non-stationary ideal NS_<kappa>lambda under cardinal arithmetic assumptions.

(1)我们将两个伯努利数的乘积之和的著名公式推广到Garlitz的q-伯努利数的公式。(2)我们给出了附加到形式群的q-伯努利数的Kaneko类型的递推公式。(3)提出了KdV的线性化隐式有限差分方法，并将其直接推广到KP方程。我们研究了该方法的精度阶，并证明该方法是无条件线性稳定的。（4）最初由Deutsch提出的量子图灵机的halt方案经过精确重新表述，并被证明可以在不破坏计算的情况下工作。（5）我们考虑带反馈的连续时间高斯信道，并研究互信息和信道容量的问题。虽然在大多数以前的工作中，对高斯噪声施加了一些条件，但在本文中，我们不需要对高斯噪声施加任何特殊条件。我们推导了通过带反馈的高斯信道传输的互信息的公式。然后我们证明信道的容量是通过线性方案实现的，更准确地说，是通过借助线性反馈发送高斯消息来实现的。我们还展示了有关通道容量的一些不等式。(6)我们提出了一个简单的条件，使理想不会陡峭。通过这个条件，我们没有表现出 P_<kappa>lambda 的基本理想的陡峭性，特别是基数算术假设下的非平稳理想 NS_<kappa>lambda。