Posted on Categories:Cryptography, 密码学, 数学代写

# 数学代写|密码学代写Cryptography Theory代考|CSE664 Non-polynomial Time Algorithms

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|密码学Cryptography Theory代考|Non-polynomial Time Algorithms

We next discuss algorithms whose running times are not the order of any polynomial. These “non-polynomial” time algorithms cannot be considered practical or efficient on inputs that are very large.

As an example, we consider an algorithm that decides whether a given integer $n \geq 2$ is prime or composite. In other words, our algorithm computes the function
$$f:{2,3,4,5, \ldots} \rightarrow{\mathrm{YES}, \mathrm{NO}}$$
defined as
$$f(n)=\left{\begin{array}{l} \text { YES if } n \text { is a prime number } \ \mathrm{NO} \text { if } n \text { is a composite number. } \end{array}\right.$$
The algorithm is based on the following well-known fact from number theory.
Proposition 4.3.1 Let $n$ be a composite number. Then $n$ has an integer factor $\leq$ $\sqrt{n}$.

Proof Write $n=a b$ for $1\sqrt{n}$. Then $b>\sqrt{n}$, thus $a b>\sqrt{n} \cdot \sqrt{n}=n$, a contradiction.
Thus if $n$ has no integer factors $\leq \sqrt{n}$, then it is prime.

## 数学代写|密码学Cryptography Theory代考|Complexity Classes P, PP, BPP

Definition 4.4.1 A decision problem $\mathcal{D}$ is a problem whose solution is either “yes” or “no”. An instance of the decision problem is an input for the problem that needs to be decided. If $S$ is the set of instances of decision problem $\mathcal{D}$, then $\mathcal{D}$ can be viewed as a function $f: S \rightarrow{\mathrm{YES}, \mathrm{NO}} ; f$ is the function associated to $\mathcal{D}$.
Example 4.4.2 Determining whether a given integer is prime or composite is a decision problem,
$\mathcal{D}:$ given integer $n \geq 2$, decide whether $n$ is prime or composite The set of instances for $\mathcal{D}$ is $S={2,3,4, \ldots}$, the associated function is
$$f(n)=\left{\begin{array}{l} \text { YES if } n \text { is a prime number } \ \mathrm{NO} \text { if } n \text { is a composite number } \end{array}\right.$$
Algorithms are used to solve (or decide) decision problems; an algorithm that solves a decision problem actually computes its associated function. For instance, PRIME solves the decision problem $\mathcal{D}$ of Example 4.4.2; PRIME computes the function $f(n)$ of Example 4.4.2.

Decision problems that can be solved by efficient, practical algorithms form a special subclass of problems.

## 数学代写|密码学Cryptography Theory代考|非多项式时间算法

$$f:{2,3,4,5, \ldots} \rightarrow{\mathrm{YES}, \mathrm{NO}}$$

$$f(n)=\left{\begin{array}{l} \text { YES if } n \text { is a prime number } \ \mathrm{NO} \text { if } n \text { is a composite number. } \end{array}\right.$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。