### 数学代写|理论计算机代写theoretical computer science代考|Implementation and Experimental Results

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|理论计算机代写theoretical computer science代考|Implementation and Experimental Results

We implemented our heuristics as a package in the PRISM model checker. Our implementations are based on sparse engine of PRISM [9] which is developed in $\mathrm{C}$ and are available in [18]. We used several standard case studies which have been used in previous works $[2,4,10,13,15,16]$. We compare the running time of our heuristics with the running time of well-known previous methods. We only focus on the running time of the iterative computations for quantitative properties. We exclude the running times for model constructions that are the same for all methods. The running time of the graph-based pre-computation are negligible in appropriate implementations [7]. For SCC-based methods and our Dirac-based ones, the reported times include the running times for SCC decomposition and Dirac-based reductions. All benchmarks have been run on a machine with Corei7 CPU (2.8 GHz, 4 main cores) and 8 GB RAM running Ubuntu 18. We use Consensus, Zeroconf, finewire_abstract, brp, nand and Crowds case studies for comparing the performance of iterative methods for reachability probabilities and use Wlan, CSMA, Israeli-jalefon and Leader cases for expected rewards. These case studies are explained in $[4,15,16]$. More details about our experiments and model parameters are available as log-files in [18]. Although there are several other standard case studies, their graphical structure do not have any cycle and a topological backward iterative method can be used to computed their underlying properties in linear time $[13,14]$. Hence, we focus on the case studies of Table 1 , where have several non-trivial cycles.

We consider the running time of the standard iterative methods and well known improved techniques from previous works. To perform a fair comparison, we use sparse engine of PRISM for all experiments and we also implemented topological (SCC-based) method for this engine. In this case, we use MPI to solve each SCC. For learning-based methods, we use the implementation that is proposed in [15] and for backward value iteration, we implement the proposed method from [14]. For all case studies, we consider $\epsilon=10^{-8}$ as the threshold.
Table 1 shows the running time of the iterative methods for MDP models. For the SCC-based method, we use MPI to approximate the reachability probability values of each SCCs. All times are in seconds. We use * where a method does not terminate after an hour. For consensus, Israeli-jalefon, Leader and Wlan models, the running time of SCC-based method is less than the others. In these cases, we use our Dirac-based method to reduce the running time of the computations for each SCC. The results show that for these two classes, our technique is faster than the other methods. The learning-based method is faster than other methods for zeroconf cases with $\mathrm{N}=20$. For firewire case studies, $\mathrm{SCC}$ based and backward value iteration methods are much faster than the standard iterative methods. In this case Dirac-based method for MPI (without SCC decomposition) works better than the other methods.

## 数学代写|理论计算机代写theoretical computer science代考|Learning for Network Traffic Classification

Characterizing the network traffic and identifying running applications play an important role in several network administration tasks such as protecting against malicious behaviors, firewalling, and balancing bandwidth usage. Recently, dynamic port assignment and encryption protocol usage have considerably reduced the performance of the classic traffic classification methods, including port-based and deep packet inspection. This leads researchers to apply Machine-Learning techniques and behavioral pattern detection for traffic classification. Machine-Learning approaches classify network traffic based on statistical

features with the granularity of flow [1,2] or packet [3], and hence, they ignore temporal relations among flows, and as a result, their false positive rates are not negligible although they are fast. In behavioral classification methods [46 , an expert extracts specific behavioral aspects of a particular application or application type for the classification purpose. For instance, link establishment topology was used as the distinctive metric to classify P2P-TV traffic in [5].
Assuming a packet trace as a word of the language of an application, one can derive an automaton modeling the traffic behavior of that application. Automata learning approaches have been recently used to automatically derive the model of applications $[7,8]$, network protocols $[9,10]$, or Botnet behavior [8]. The alphabets of the learned automata are either manually defined by domain experts which is not straightforward, or in terms of packets which may cause overfitting. As some packets always appear together, we can consider a sequence of related packets together as a symbol of the alphabet. To this aim, we apply machine learning techniques to automatically define the alphabet set based on the timing and statistical features of packets.

The derived automata are used for traffic classification. A packet trace is classified into an application if the model of that application accepts it. Using automata learning methods, the classification problem is constrained to observe the complete trace of an application to verdict its acceptance/rejection. To tackle this challenge, inspired by [11], we upgrade the detection of an application based on partial observation of a trace, a window of size $k$, and derive a model that accepts a k-Testable language in the Strict Sense (k-TSS) [12]. K-TSS, a class of regular languages, also known as window language, allows to locally accept or reject a word by a sliding window parser of size $k$. We relax the acceptance condition of automata learning using machine learning by defining a proximity metric to be compatible with the local essence of the learned language. The proposed proximity metric is defined as a distance function. We have implemented our approach in a framework called Network Traffic Language learner, NeTLang. We evaluate the performance of our approach by applying it to real-world network traffic and compare it with machine and automata learning approaches. We achieved F1-Measure of $97 \%$ for both application identification and traffic characterization tasks. In summary, first, we learn the alphabet using a machine learning technique. Then, the network language is learned through an automata learning approach. Finally, the classifier identifies the classes based on our defined distance metrics on the input and the learned models. Our method makes these contributions: 1) Utilizing locally testable language learning in the traffic classification problem, 2) Extracting the domain-based alphabet automatically, 3) Upgrading the word acceptance by a new proximity metric. With these contributions, the following improvements are brought into traffic classification:

• Considering a sequence of related packets as the appropriate granularity of the problem, instead of per-packet detection which is too fine-grained or per-flow detection which is too coarse-grained,Providing highly accurate models for applications as our automata learning approach considers the temporal relation among flows and the way they are interleaved,
• Decreasing the classification time by considering only some first packets of a trace with a help of a novel distance function.

## 数学代写|理论计算机代写theoretical computer science代考|Background on Automata Learning

In this section, we provide some background on automata learning concepts used in our methodology. Learning a regular language from given positive samples (words belonging to the language) is a common problem in grammatical inference. To solve this problem, many algorithms were proposed to find the smallest deterministic finite automaton (DFA) that accepts the positive examples. In this paper, we focus on learning k-testable languages in the strict sense, a subset of a regular language, called k-TSS, initially was introduced by [12]. In such a language, words are determined by allowed three sets of prefixes and suffixes of length $k-1$ and substrings of length $k$. It has been proven that it is possible to learn k-TSS languages in the limit [13]. To learn this language, the only effort is to scan the accepting words while simultaneously constructing the allowed three set. The locally testable feature of this language makes it appropriate for network traffic classification and other domains, such as pattern recognition [14] and DNA sequence analysis [15]. In the following, we provide the formal definition of k-TSS language taken from [16].

Definition 1 (k-test Vector). Let $k>0, a$-test vector is determined by $a$ 5 -tuple $Z=\langle\Sigma, I, F, T, C\rangle$ where

• $\Sigma$ is a finite alphabet,
• $I \subseteq \Sigma^{(k-1)}$ is a set of allowed prefixes of length less than $k$,
• $F \subseteq \Sigma^{(k-1)}$ is a set of allowed suffixes of length less than $k$,
• $T \subseteq \Sigma^{k}$ is a set of allowed segments, and
• $C \subseteq \Sigma^{0$. Then Language $\mathcal{L}(Z)$ in the strict sense $(k-T S S)$ is computed as:
$$\mathcal{L}(Z)=\left[\left(I \Sigma^{} \cap \Sigma^{} F\right)-\Sigma^{}\left(\Sigma^{k}-T\right) \Sigma^{}\right] \cup C$$
For instance, consider $k=3$ and $Z=\langle\Sigma={a, b}, I={a b}, F=$ ${a b, b a}, T={a b a, a b b, b b a}, C={a b}\rangle$, then, $a b a, a b b a \in \mathcal{L}(Z)$ since they are preserving the allowed sets of $Z$, while $b a b, a b b, a b a b, a$ do not belong to $\mathcal{L}(z)$ because, in order, they violate $I \mathrm{~ ( b a ~}$ $(a \notin C$ ). To construct the k-test vector of a language, we scan the accepted word by a k-size frame. By scanning the word $a b b a$ by a 3 -size frame, $a b, b a$, and $a b b, b b a$ are added to $I, F$, and $T$, respectively.

In our problem, we produce words such that their length is greater than or equal to $k$. It means that $C$ always is empty. Hence, for simplicity, we eliminate $C$ from the k-TSS vector for the rest of the paper.、

## 数学代写|理论计算机代写theoretical computer science代考|Learning for Network Traffic Classification

• 考虑一系列相关数据包作为问题的适当粒度，而不是太细粒度的每个数据包检测或太粗粒度的每个流检测，为我们的自动机学习方法考虑的应用程序提供高精度模型流之间的时间关系以及它们交错的方式，
• 在新的距离函数的帮助下，通过仅考虑跟踪的一些第一个数据包来减少分类时间。

## 数学代写|理论计算机代写theoretical computer science代考|Background on Automata Learning

• Σ是一个有限的字母表，
• 一世⊆Σ(ķ−1)是一组长度小于的允许前缀ķ,
• F⊆Σ(ķ−1)是一组允许的长度小于的后缀ķ,
• 吨⊆Σķ是一组允许的段，并且
• $C \subseteq \Sigma^{0.吨H和n大号一种nG在一种G和\数学{L} (Z)一世n吨H和s吨r一世C吨s和ns和(千吨不锈钢)一世sC这米p在吨和d一种s:大号(从)=[(一世Σ∩ΣF)−Σ(Σķ−吨)Σ]∪CF这r一世ns吨一种nC和,C这ns一世d和rk=3一种ndZ=\langle\Sigma={a, b}, I={ab}, F={ab, ba}, T={aba, abb, bba}, C={ab}\rangle,吨H和n,aba, abba \in \mathcal{L}(Z)s一世nC和吨H和是一种r和pr和s和r在一世nG吨H和一种ll这在和ds和吨s这F从,在H一世l和bab, abb, abab, 一个d这n这吨b和l这nG吨这\数学{L} (z)b和C一种在s和,一世n这rd和r,吨H和是在一世这l一种吨和我 \mathrm{~ ( ba ~}(a \notin C).吨这C这ns吨r在C吨吨H和ķ−吨和s吨在和C吨这r这F一种l一种nG在一种G和,在和sC一种n吨H和一种CC和p吨和d在这rdb是一种ķ−s一世和和Fr一种米和.乙是sC一种nn一世nG吨H和在这rd阿爸b是一种3−s一世和和Fr一种米和,呸呸呸,一种ndabb, bba一种r和一种dd和d吨这如果,一种ndT$，分别。

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