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第305行： − − === Data processing networks === − − the length of the longest path, from the n-th node added to the network to the first node in the network, scales as <math>\ln(n)</math>. − − 最长路径的长度，从添加到网络的第 n 个节点到网络中的第一个节点，缩放为 < math > ln (n) </math > 。 − − A directed acyclic graph may be used to represent a network of processing elements. In this representation, data enters a processing element through its incoming edges and leaves the element through its outgoing edges. − − − − For instance, in electronic circuit design, static [[combinational logic]] blocks can be represented as an acyclic system of [[logic gate]]s that computes a function of an input, where the input and output of the function are represented as individual [[bit]]s. In general, the output of these blocks cannot be used as the input unless it is captured by a register or state element which maintains its acyclic properties.<ref>{{citation|title=Timing|first=Sachin|last=Sapatnekar|publisher=Springer|year=2004|isbn=978-1-4020-7671-8|page=133|url=https://books.google.com/books?id=fL9k-VkZVr0C&pg=PA133}}.</ref> Electronic circuit schematics either on paper or in a database are a form of directed acyclic graphs using instances or components to form a directed reference to a lower level component. Electronic circuits themselves are not necessarily acyclic or directed. − − Directed acyclic graphs may also be used as a compact representation of a collection of sequences. In this type of application, one finds a DAG in which the paths form the given sequences. When many of the sequences share the same subsequences, these shared subsequences can be represented by a shared part of the DAG, allowing the representation to use less space than it would take to list out all of the sequences separately. For example, the directed acyclic word graph is a data structure in computer science formed by a directed acyclic graph with a single source and with edges labeled by letters or symbols; the paths from the source to the sinks in this graph represent a set of strings, such as English words. Any set of sequences can be represented as paths in a tree, by forming a tree vertex for every prefix of a sequence and making the parent of one of these vertices represent the sequence with one fewer element; the tree formed in this way for a set of strings is called a trie. A directed acyclic word graph saves space over a trie by allowing paths to diverge and rejoin, so that a set of words with the same possible suffixes can be represented by a single tree vertex. − − 有向无环图也可用作序列集合的紧凑表示。在这种类型的应用程序中，人们会找到一个 DAG，其中的路径形成给定的序列。当许多序列共享相同的子序列时，这些共享子序列可以由 DAG 的一个共享部分来表示，这使得这种表示比单独列出所有序列所需要的空间更少。例如，有向无环词图是计算机科学中的一种数据结构，由一个单源的有向无环图构成，其边缘用字母或符号标记; 在这个图中，从源到汇的路径表示一组字符串，例如英语单词。任何一组序列都可以表示为树中的路径，方法是为序列的每个前缀形成一个树顶点，并使其中一个顶点的父顶点表示只有一个元素的序列; 对于一组字符串以这种方式形成的树称为 trie。有向无环词图允许路径发散和重新连接，从而在一个三元图上节省空间，这样一组可能具有相同后缀的词可以由一个树顶点表示。 − − − − [[Dataflow programming]] languages describe systems of operations on [[data stream]]s, and the connections between the outputs of some operations and the inputs of others. These languages can be convenient for describing repetitive data processing tasks, in which the same acyclically-connected collection of operations is applied to many data items. They can be executed as a [[parallel algorithm]] in which each operation is performed by a parallel process as soon as another set of inputs becomes available to it.<ref>{{citation|title=Programming Symposium|series=Lecture Notes in Computer Science|volume=19|year=1974|pages=362–376|contribution=First version of a data flow procedure language|first=Jack B.|last=Dennis|doi=10.1007/3-540-06859-7_145|isbn=978-3-540-06859-4}}.</ref> − − The same idea of using a DAG to represent a family of paths occurs in the binary decision diagram, a DAG-based data structure for representing binary functions. In a binary decision diagram, each non-sink vertex is labeled by the name of a binary variable, and each sink and each edge is labeled by a 0 or 1. The function value for any truth assignment to the variables is the value at the sink found by following a path, starting from the single source vertex, that at each non-sink vertex follows the outgoing edge labeled with the value of that vertex's variable. Just as directed acyclic word graphs can be viewed as a compressed form of , binary decision diagrams can be viewed as compressed forms of decision trees that save space by allowing paths to rejoin when they agree on the results of all remaining decisions. − − 使用 DAG 表示一系列路径的同样想法也出现在二元决策图中，这是一个基于 dags 的数据结构，用于表示二进制函数。在二元决策图中，每个无汇点都用一个二进制变量的名称标记，每个汇点和每条边都用一个0或1标记。任何对变量进行真值赋值的函数值，都是指从单个源顶点开始，沿着一条路径，在每个非汇顶点上沿着标有该顶点变量值的外向边缘，在汇处找到的值。正如有向无环字图可以看作是一种压缩形式，二叉决策图可以看作是一种压缩形式的决策树，通过允许路径在所有剩余决策的结果一致时重新连接来节省空间。 − − − − In [[compiler]]s, straight line code (that is, sequences of statements without loops or conditional branches) may be represented by a DAG describing the inputs and outputs of each of the arithmetic operations performed within the code. This representation allows the compiler to perform [[common subexpression elimination]] efficiently.<ref>{{citation|title=Advanced Backend Optimization|first1=Sid|last1=Touati|first2=Benoit|last2=de Dinechin|publisher=John Wiley & Sons|year=2014|isbn=978-1-118-64894-0|page=123|url=https://books.google.com/books?id=nO2-AwAAQBAJ&pg=PA123}}.</ref> At a higher level of code organization, the [[acyclic dependencies principle]] states that the dependencies between modules or components of a large software system should form a directed acyclic graph.<ref>{{citation|title=Large-Scale Software Architecture: A Practical Guide using UML|first1=Jeff|last1=Garland|first2=Richard|last2=Anthony|publisher=John Wiley & Sons|year=2003|isbn=9780470856383|page=215|url=https://books.google.com/books?id=_2oQLLSqZ88C&pg=PA215}}.</ref> − − − − [[Feedforward neural network]]s are another example. − −
→Data processing networks
普莱斯模型过于简单，不可能成为引文网络的现实模型，但它足够简单，可以为其某些属性提供分析解。其中许多问题可以通过使用从价格模型(Barabási-Albert 模型)的无向版本得出的结果来找到。然而，由于 Price 的模型给出了一个有向无环图，所以在寻找有向无圈图所特有的性质的解析计算时，它是一个很有用的模型。比如说,
普莱斯模型过于简单，不可能成为引文网络的现实模型，但它足够简单，可以为其某些属性提供分析解。其中许多问题可以通过使用从价格模型(Barabási-Albert 模型)的无向版本得出的结果来找到。然而，由于 Price 的模型给出了一个有向无环图，所以在寻找有向无圈图所特有的性质的解析计算时，它是一个很有用的模型。比如说,
=== Causal structures ===
=== Causal structures ===