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Propositional Directed Acyclic Graph
A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph of the following form: * Leaves are labeled with \top (true), \bot (false), or a Boolean variable. * Non-leaves are \bigtriangleup (logical and), \bigtriangledown (logical or) and \Diamond (logical not). * \bigtriangleup- and \bigtriangledown-nodes have at least one child. * \Diamond-nodes have exactly one child. Leaves labeled with \top (\bot) represent the constant Boolean function which always evaluates to 1 (0). A leaf labeled with a Boolean variable x is interpreted as the assignment x=1, i.e. it represents the Boolean function which evaluates to 1 if and only if x=1. The Boolean function represented by a \bigtriangleup-node is the one that evaluates to 1, if and only if the Boolean function of all its children evaluate to 1. Similarly, a \bigtriangledown-node represents the Boolean function tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a ''vectorial'' or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Acyclic Graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs. Definitions A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Decision Diagram
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed representation, i.e. without decompression. Similar data structures include negation normal form (NNF), Zhegalkin polynomials, and propositional directed acyclic graphs (PDAG). Definition A Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several (decision) nodes and two terminal nodes. The two terminal nodes are labeled 0 (FALSE) and 1 (TRUE). Each (decision) node u is labeled by a Boolean variable x_i and has two child nodes called low child and high child. The edge from node u to a low (or high) child represents an assignment of the value FALSE (or TRUE, respectively) to variable x_i. Such a BDD is ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negation Normal Form
In mathematical logic, a formula is in negation normal form (NNF) if the negation operator (\lnot, ) is only applied to variables and the only other allowed Boolean operators are conjunction (\land, ) and disjunction (\lor, ). Negation normal form is not a canonical form: for example, a \land (b\lor \lnot c) and (a \land b) \lor (a \land \lnot c) are equivalent, and are both in negation normal form. In classical logic and many modal logics, every formula can be brought into this form by replacing implications and equivalences by their definitions, using De Morgan's laws to push negation inwards, and eliminating double negations. This process can be represented using the following rewrite rules (Handbook of Automated Reasoning 1, p. 204): :\begin A \Rightarrow B &~\to~ \lnot A \lor B \\ \lnot (A \lor B) &~\to~ \lnot A \land \lnot B \\ \lnot (A \land B) &~\to~ \lnot A \lor \lnot B \\ \lnot \lnot A &~\to~ A \\ \lnot \exists x A &~\to~ \forall x \lnot A \\ \lnot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BDD Simple
Gwak Bo-seong (, born March 1, 1999), better known as Bdd, is a South Korean professional ''League of Legends'' player for KT Rolster. He is a two-time LCK regular season MVP, receiving the title in the 2017 summer and 2018 spring splits. Bdd's signature champions are considered to be Galio, Azir, Taliyah, Orianna although his favourite champion is Zed. Career Bdd stands for (), which means "rice thief". Bdd joined CJ Entus as a substitute mid laner in April 2015 but was unable to play for them due to being underage. Bdd was hyped as "super-rookie" and the biggest Korean mid laner prospect after Faker before his debut. He finally turned 17 on March 1, 2016, and he made his competitive debut in the 2016 LCK Spring on March 2 in a series against Kongdoo Monster, which CJ won 2–1. He finished the first competitive season at 8th place. CJ Entus had a very poor showing in the 2016 LCK Summer season, going 3-15 total in set score and relegated first time in history. Bdd along ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BDD2pdag
Gwak Bo-seong (, born March 1, 1999), better known as Bdd, is a South Korean professional '' League of Legends'' player for KT Rolster. He is a two-time LCK regular season MVP, receiving the title in the 2017 summer and 2018 spring splits. Bdd's signature champions are considered to be Galio, Azir, Taliyah, Orianna although his favourite champion is Zed. Career Bdd stands for (), which means "rice thief". Bdd joined CJ Entus as a substitute mid laner in April 2015 but was unable to play for them due to being underage. Bdd was hyped as "super-rookie" and the biggest Korean mid laner prospect after Faker before his debut. He finally turned 17 on March 1, 2016, and he made his competitive debut in the 2016 LCK Spring on March 2 in a series against Kongdoo Monster, which CJ won 2–1. He finished the first competitive season at 8th place. CJ Entus had a very poor showing in the 2016 LCK Summer season, going 3-15 total in set score and relegated first time in history. Bdd a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BDD2pdag Simple
Gwak Bo-seong (, born March 1, 1999), better known as Bdd, is a South Korean professional '' League of Legends'' player for KT Rolster. He is a two-time LCK regular season MVP, receiving the title in the 2017 summer and 2018 spring splits. Bdd's signature champions are considered to be Galio, Azir, Taliyah, Orianna although his favourite champion is Zed. Career Bdd stands for (), which means "rice thief". Bdd joined CJ Entus as a substitute mid laner in April 2015 but was unable to play for them due to being underage. Bdd was hyped as "super-rookie" and the biggest Korean mid laner prospect after Faker before his debut. He finally turned 17 on March 1, 2016, and he made his competitive debut in the 2016 LCK Spring on March 2 in a series against Kongdoo Monster, which CJ won 2–1. He finished the first competitive season at 8th place. CJ Entus had a very poor showing in the 2016 LCK Summer season, going 3-15 total in set score and relegated first time in history. Bdd a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Satisfiability Problem
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called ''satisfiable''. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is ''unsatisfiable''. For example, the formula "''a'' AND NOT ''b''" is satisfiable because one can find the values ''a'' = TRUE and ''b'' = FALSE, which make (''a'' AND NOT ''b'') = TRUE. In contrast, "''a'' AND NOT ''a''" is unsatisfiable. SAT is the first problem that was proved to be NP-complete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proposition (mathematics)
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Data Structures
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Statistical graphics Statistical graphics, also known as statistical graphical techniques, are graphic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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