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## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|CS154 Extended Markovian Process Algebra

avatest.org理论计算机Theoretical computer science代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest.org™， 最高质量的理论计算机Theoretical computer science作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此理论计算机Theoretical computer science作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

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## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|Extended Markovian Process Algebra

In this section we revisit EMPA $\mathrm{gr}_{\text {[4] }}$, a Markovian process algebra extended with prioritized/weighted immediate actions à la GSPN [1] in which interprocess communication is based on a multiway generative-reactive [5] synchronization mechanism.

In $\mathrm{EMPA}_{\mathrm{gr}}$ every action is durational, hence it is represented as a pair $$, where a is the action name and \tilde{\lambda} is the action rate. There are three kinds of actions: exponentially timed, immediate, and passive. Exponentially timed actions are of the form$$ with $\lambda \in \mathbf{R}_{>0}$. The duration of each such action is exponentially distributed with parameter equal to the action rate (hence its average duration is the inverse of its rate). Whenever several exponentially timed actions are enabled, the race policy is adopted, hence the fastest action is the one that is executed. As a consequence, the execution probability of an exponentially timed action is proportional to its rate.

Immediate actions are of the form $\left\langle a, \infty_{l, w}>\right.$, where $l \in \mathbf{N}{>0}$ is the priority level and $w \in \mathbb{R}{>0}$ is the weight. Each immediate action has duration zero and takes precedence over exponentially timed actions (which are assumed to have priority level 0 ). Whenever several immediate actions are enabled, the generative preselection policy is adopted, i.e. each action is given an execution probability proportional to its weight provided that it has the highest priority level within the considered action set.

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|Weak Extended Markovian Bisimilarity

A behavioral equivalence typically used for reasoning about Markovian process terms is Markovian bisimilarity [7]. In particular, an extension of it has been defined in Refs. 3,4 in order to deal with prioritized/weighted immediate actions. The limitation of extended Markovian bisimilarity is that it does not provide any abstraction mechanism. In fact, actions of the form $<\tau, \infty_{l, w}>$ are invisible and take no time, hence they are unimportant both from the functional viewpoint and from the performance viewpoint. Thus they should not be considered when comparing the behavior of two terms.

After recalling the definition of extended Markovian bisimilarity, we introduce a weak variant of it that abstracts from internal immediate actions. Then we show that this weak variant is a congruence and admits a sound and complete axiomatization for the class of well-prioritized process terms.

## 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。

Posted on Categories:数学代写, 理论计算机

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|CSCI270 A polynomial-time algorithm for paths with a bounded number of colors

avatest.org理论计算机Theoretical computer science代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest.org™， 最高质量的理论计算机Theoretical computer science作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此理论计算机Theoretical computer science作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

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## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|A polynomial-time algorithm for paths with a bounded number of colors

We complement here the results of the two preceding sections by showing that the MIN-CC problem for paths is polynomial-time solvable in case the motif is built upon a fixed number of colors. Observe, however, that each color may still have an unbounded number of occurrences in the motif.

In what follows we describe a dynamic programming algorithm for this case. The basic idea of our approach is as follows. Suppose we are left by the algorithm with the problem of finding an occurrence of a submotif $\mathcal{M}^{\prime} \subseteq \mathcal{M}$ in the subpath $G^{\prime}$ of $G$ induced by ${i, i+1, \ldots, j}, 1 \leq i<j \leq n$. Furthermore, suppose that any occurrence of $\mathcal{M}^{\prime}$ in $G^{\prime}$ results in at least $k^{\prime}$ connected components. This minimum number of occurrences $k^{\prime}$ can be computed as follows. Assume that we have found one leftmost connected component $C_{\text {left }}$ of the occurrence of $\mathcal{M}^{\prime}$ in $G^{\prime}$ and let $i_{2}, i \leq i_{2}<j$, be the rightmost (according to the natural order of the vertices) vertex of $C_{\text {left }}$. Let $\mathcal{M}^{\prime \prime}$ be the motif obtained from $\mathcal{M}^{\prime}$ by subtracting to each color $c_{\ell} \in \mathcal{C}$ the number of occurrences of color $c_{\ell}$ in the leftmost connected component $C_{\text {left }}$. Then the occurrence of $\mathcal{M}^{\prime}$ in $G^{\prime}$ is given by $\left{i_{2}+1, i_{2}+2, \ldots, j\right}$, which results in $k^{\prime}-1$ connected components. From an optimization point of view, the problem thus reduces to finding a subpath $\left{i_{1}, i_{1}+\right.$ $\left.1, \ldots, i_{2}\right}, i \leq i_{1} \leq i_{2}<j$, such that the occurrence of the motif $\mathcal{M}^{\prime \prime}$ modified according to the colors in $\left{i_{1}, i_{1}+1, \ldots, i_{2}\right}$ in the subpath induced by $\left{i_{2}+\right.$ $\left.1, i_{2}+2, \ldots, j\right}$ results in a minimum number of connected components.

Let $(G, \mathcal{M})$ be an instance of the MıN-CC problem where $G$ is a (vertexcolored) path built upon the set of colors $\mathcal{C}$. For ease of exposition, write $\mathbf{V}(G)=$ ${1,2, \ldots, n}$ and $q=|\mathcal{C}|$. We denote by $m_{i}$ the number of occurrences of color $c_{i} \in \mathcal{C}$ in $\mathcal{M}$. Clearly, $\sum_{c_{i} \in \mathcal{C}} m_{i}=|\mathcal{M}|$. We now introduce our dynamic programming table $T$. Define $T\left[i, j ; p_{1}, p_{2}, \ldots, p_{q}\right], 1 \leq i \leq j \leq n$ and $0 \leq p_{\ell} \leq m_{\ell}$ for $1 \leq \ell \leq q$, to be the minimum number of connected components in the subpath of $G$ that starts at node $i$, ends at node $j$ and that covers $p_{\ell}$ occurrences of color $c_{\ell}, 1 \leq \ell \leq q$. The base conditions are as follows:

• for all $1 \leq i \leq j \leq n, T[i, j ; 0,0, \ldots, 0]=0$ and $T\left[i, i ; p_{1}, p_{2}, \ldots, p_{q}\right]=\infty$ if $\sum_{1 \leq \ell \leq q} p_{\ell}>1$
• for all $1 \leq i \leq n, T\left[i, i ; p_{1}, p_{2}, \ldots, p_{q}\right]=\infty$ if $\sum_{1 \leq \ell \leq q} p_{\ell}=1$ and $\lambda(i) \neq c_{\ell}$ and $p_{\ell}=1$, and $T\left[i, i ; p_{1}, p_{2}, \ldots, p_{q}\right]=1$ if $\sum_{1 \leq \ell \leq q} p_{\ell}=$ 1 and $\lambda(i)=c_{\ell}$ and $p_{\ell}=1$.

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|Hardness of approximation for trees

We investigate in this section approximation issues for restricted instances of the MIN-CC problem. Unfortunately, as we shall now prove, it turns out that, even if $\mathcal{M}$ is a set and $G$ is a tree, the MıN-CC problem cannot be approximated within ratio $c \log n$ for some constant $c>0$, where $n$ is the size of the target graph $G$. As a side result, we prove that the MIN-CC problem is W[2]-hard when parameterized by the number of connected components of the occurrence of $\mathcal{M}$ in the target graph $G$.

At the core of our proof is an L-reduction [12] from the SET-COVER problem. Let $I$ be an arbitrary instance of the SET-COVER problem consisting of a universe set $X(I)=\left{x_{1}, x_{2}, \ldots, x_{n}\right}$ and a collection of sets $\mathcal{S}(I)=S_{1}, S_{2}, \ldots, S_{m}$, each over $X(I)$. For each $1 \leq i \leq m$, write $t_{i}=\left|S_{i}\right|$ and denote by $e_{j}\left(S_{i}\right)$, $1 \leq j \leq t_{i}$, the $j$-th element of $S_{i}$. For ease of exposition, we present the corresponding instance of the MIN-CC problem as a rooted tree $G$. We construct the tree $G$ as follows (see Fig. 1). Define a root $r$ and vertices $S_{1}^{\prime}, S_{2}^{\prime}, \ldots, S_{m}^{\prime}$ such that each vertex $S_{i}^{\prime}$ is connected to the root $r$. For each $S_{i}^{\prime}$ define the subtree $G\left(S_{i}^{\prime}\right)$ rooted at $S_{i}^{\prime}$ as follows: each vertex $S_{i}^{\prime}$ has a unique child $S_{i}$ and each vertex $S_{i}$ has children $e_{1}\left(S_{i}\right), e_{2}\left(S_{i}\right), \ldots, e_{t_{i}}\left(S_{i}\right)$. The set of colors $\mathcal{C}$ is defined as follows: $\mathcal{C}=\left{c\left(S_{i}\right): 1 \leq i \leq m\right} \cup\left{c\left(x_{j}\right): 1 \leq j \leq n\right} \cup{c(r)}$. The coloring mapping $\lambda: \mathbf{V}(G) \rightarrow \mathcal{C}$ is defined by: $\lambda\left(S_{i}\right)=\lambda\left(S_{i}^{\prime}\right)=c\left(S_{i}\right)$ for $1 \leq i \leq m$, $\lambda\left(x_{j}\right)=c\left(x_{j}\right)$ for $1 \leq j \leq n$ and $\lambda(r)=c(r)$. The motif $\mathcal{M}$ is the set defined as follows: $\mathcal{M}=\left{c\left(S_{i}\right): 1 \leq i \leq m\right} \cup\left{c\left(x_{i}\right): 1 \leq i \leq n\right} \cup{c(r)}$.

## 数学代写|理论计算机代写 THEORETICAL COMPUTER SCIENCE代写|A polynomial-time algorithm for paths with a bounded number of colors

\left 的分隔符缺失或无法识别，，这样主题的出现 $\mathcal{M}^{\prime \prime}$ 根据颜色修改
lleft 的分隔符缺失或无法识别

\left 的分隔符笡失或无法识别

## 数学代写|理论计算机代写 THEORETICAL COMPUTER SCIENCE代写|Hardness of approximation for trees

\left 的分隔符缺失或无法识别 $\quad$ 着色映射 $\lambda: \mathbf{V}(G) \rightarrow \mathcal{C}$ 定义为: $\lambda\left(S_{i}\right)=\lambda\left(S_{i}^{\prime}\right)=c\left(S_{i}\right)$ 为了 $1 \leq i \leq m, \lambda\left(x_{j}\right)=c\left(x_{j}\right)$ 为了 $1 \leq j \leq n$ 和 $\lambda(r)=c(r)$. 主 题, $\mathcal{M}$ 是定义如下的集合：\left 的分隔符筷失或无法识别

## 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。

Posted on Categories:数学代写, 理论计算机

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|CSCIE121 Fixed-parameter algorithms

avatest.org理论计算机Theoretical computer science代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。avatest.org™， 最高质量的理论计算机Theoretical computer science作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此理论计算机Theoretical computer science作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

avatest.org™ 为您的留学生涯保驾护航 在网课代修方面已经树立了自己的口碑, 保证靠谱, 高质且原创的网课代写服务。我们的专家在理论计算机Theoretical computer science代写方面经验极为丰富，各种理论计算机Theoretical computer science相关的作业也就用不着 说。

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|The MIN-CC problem is fixed-parameter tractable

We only sketch the fixed-parameter tractability result. Let $G$ be a graph and $k$ be a positive integer. Recall that a family $\mathcal{F}$ of functions from $\mathbf{V}(G)$ to ${1,2, \ldots, k}$ is perfect if for any subset $V \subseteq \mathbf{V}(G)$ of $k$ vertices there is a function $f \in \mathcal{F}$ which is injective on $V[1]$. Let $(G, \mathcal{M})$ be an instance of the MıN-CC problem, where $\mathcal{M}$ is a motif of size $k$. Then there is an occurrence of $\mathcal{M}$ in $G$, say $V \subseteq \mathbf{V}(G)$, that results in a minimum number of connected components. Furthermore, suppose we are provided with a perfect family $\mathcal{F}$ of functions from $\mathbf{V}(G)$ to ${1,2, \ldots, k}$. Since $\mathcal{F}$ is perfect, we are guaranteed that at least one function in $\mathcal{F}$ assigns $V$ with $k$ distinct labels. Let $f \in \mathcal{F}$ be such a function. We now turn to defining a dynamic programming table $T$ indexed by vertices of $G$ and subsets of ${1,2, \ldots, k}$. For any $v \in \mathbf{V}(G)$ and any $L \subseteq{1,2, \ldots, k}$, we define $T_{L}[v]$ to be the family of all motifs $\mathcal{M}^{\prime} \subseteq \mathcal{M},\left|\mathcal{M}^{\prime}\right|=|L|$, for which there exists an exact occurrence of $\mathcal{M}^{\prime}$ in $G$, say $V$, such that $v \in V$ and the set of (unique) labels that $f$ assigns to $V$ is exactly $L$. We need the following lemma [8].

## 数学代写|理论计算机代写THEORETICAL COMPUTER SCIENCE代写|A faster fixed-parameter algorithm for trees

We proved in Section 3 that the MıN-CC problem is APX-hard even if the target graph is a path. To complement Proposition 4.1, we give here a dynamic programming algorithm for trees that does not rely on the color-coding technique (approaches based on the color-coding technique usually suffer from bad running time performances).

Let $(G, \mathcal{M})$ be an instance of the MIN-CC problem for trees where both $G$ and $\mathcal{M}$ are built upon a set of colors $\mathcal{C}$. Let $k=|\mathcal{M}|$ and $q=|\mathcal{C}|$. Furthermore, for ease of exposition, write $\mathbf{V}(G)={1,2, \ldots, n}$ and assume $G$ is rooted at some arbitrary vertex $r(G)$.

Our dynamic programming algorithm is basically an exhaustive search procedure. The basic idea is to store – in a bottom-up fashion – for each vertex $i$ of $G$ and each submotif $\mathcal{M}^{\prime} \subseteq \mathcal{M}$ that occurs in $T(i)$, i.e., the subtree rooted at $i$, the minimum number of connected components that results in an occurrence of $\mathcal{M}^{\prime}$ in $T(i)$. More precisely, for each vertex $i$ of $G$, we compute two dynamic programming tables $X[i]$ and $Y[i]$. The dynamic programming table $X[i]$ stores all pairs $\left(\mathcal{M}^{\prime}, c\right)$, where $\mathcal{M}^{\prime} \subseteq \mathcal{M}$ is a submotif and $c$ is a positive integer, such that (1) there exists an occurrence of $\mathcal{M}^{\prime}$ in $T(i)$ that matches vertex $i,(2)$ the minimum number of connected components of an occurrence of $\mathcal{M}^{\prime}$ in $T(i)$ that matches vertex $i$ is $c$. The dynamic programming table $Y[i]$ stores all pairs $\left(\mathcal{M}^{\prime}, c\right)$, where $\mathcal{M}^{\prime} \subseteq \mathcal{M}$ is a submotif and $c$ is a positive integer, such that (1′) there exists an occurrence of $\mathcal{M}^{\prime}$ in $T(i)$ that does not match vertex $i,\left(2^{\prime}\right)$ the minimum number of connected components of an occurrence of $\mathcal{M}^{\prime}$ in $T(i)$ that does not match vertex $i$ is $c$.

## 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。