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Complexity Of Constraint Satisfaction
The complexity of constraint satisfaction is the application of computational complexity theory on constraint satisfaction. It has mainly been studied for discriminating between tractable and intractable classes of constraint satisfaction problems on finite domains. Solving a constraint satisfaction problem on a finite domain is an NP-complete problem in general. Research has shown a number of polynomial-time subcases, mostly obtained by restricting either the allowed domains or constraints or the way constraints can be placed over the variables. Research has also established a relationship between the constraint satisfaction problem and problems in other areas such as finite model theory and databases. Overview Establishing whether a constraint satisfaction problem on a finite domain has solutions is an NP complete problem in general. This is an easy consequence of a number of other NP complete problems being expressible as constraint satisfaction problems. Such other problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primal Constraint Graph
Primal may refer to: Psychotherapy * ''Primal'', the core concept in primal therapy, denotes the full reliving and cathartic release of an early traumatic experience * Primal scene (in psychoanalysis), refers to the witnessing by a young child of a sex act, usually between the parents, which traumatizes the child Mathematics * Primal, an old mathematics term for a projective hypersurface * Primal problem, a component of the duality principle in mathematical optimization theory Entertainment * "Primal" (Eureka episode), an episode of TV series ''Eureka'' * ''Primal'' (video game), an action video game for the PlayStation 2 * ''Primal'' (TV series), a 2019 animated television series * ''Primal'' (2019 film), a 2019 film starring Nicolas Cage * Optimus Primal, a character in ''Transformers'' * ''The Lost Tribe'' (2010 film), a film whose Australian DVD was entitled ''Primal'' * ''Primal'' (2010 film), an Australian horror film directed by Josh Reed * ''Far Cry Primal'', a 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Consistency
In constraint satisfaction, local consistency conditions are properties of constraint satisfaction problems related to the consistency of subsets of variables or constraints. They can be used to reduce the search space and make the problem easier to solve. Various kinds of local consistency conditions are leveraged, including node consistency, arc consistency, and path consistency. Every local consistency condition can be enforced by a transformation that changes the problem without changing its solutions. Such a transformation is called constraint propagation. Constraint propagation works by reducing domains of variables, strengthening constraints, or creating new ones. This leads to a reduction of the search space, making the problem easier to solve by some algorithms. Constraint propagation can also be used as an unsatisfiability checker, incomplete in general but complete in some particular cases. Local consistency conditions can be grouped into various classes. The original lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datalog
Datalog is a declarative logic programming language. While it is syntactically a subset of Prolog, Datalog generally uses a bottom-up rather than top-down evaluation model. This difference yields significantly different behavior and properties from Prolog. It is often used as a query language for deductive databases. In recent years, Datalog has found new application in data integration, information extraction, networking, program analysis, security, cloud computing and machine learning. Its origins date back to the beginning of logic programming, but it became prominent as a separate area around 1977 when Hervé Gallaire and Jack Minker organized a workshop on logic and databases. David Maier is credited with coining the term Datalog. Features, limitations and extensions Unlike in Prolog, statements of a Datalog program can be stated in any order. Furthermore, Datalog queries on finite sets are guaranteed to terminate, so Datalog does not have Prolog's cut operator. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E) to denote a bipartite graph whose partition has the parts U and V, with E denoting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schaefer's Dichotomy Theorem
In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem states necessary and sufficient conditions under which a finite set ''S'' of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of ''S'' are used to constrain some of the propositional variables. It is called a dichotomy theorem because the complexity of the problem defined by ''S'' is either in P or NP-complete as opposed to one of the classes of intermediate complexity that is known to exist (assuming P ≠ NP) by Ladner's theorem. Special cases of Schaefer's dichotomy theorem include the NP-completeness of SAT (the Boolean satisfiability problem) and its two popular variants 1-in-3 SAT and not-all-equal 3SAT (often denoted by NAE-3SAT). In fact, for these two variants of SAT, Schaefer's dichotomy theorem shows that their monotone versions (where negations of variables are not allowed) are also NP-complete. Original presentation Sch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multi categorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes. Etymology The term '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ladner's Theorem
In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem, shown in 1975 by Richard E. Ladner, is a result asserting that, if P ≠ NP, then NPI is not empty; that is, NP contains problems that are neither in P nor NP-complete. Since it is also true that if NPI problems exist, then P ≠ NP, it follows that P = NP if and only if NPI is empty. Under the assumption that P ≠ NP, Ladner explicitly constructs a problem in NPI, although this problem is artificial and otherwise uninteresting. It is an open question whether any "natural" problem has the same property: Schaefer's dichotomy theorem provides conditions under which classes of constrained Boolean satisfiability problems cannot be in NPI. Some problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, factoring, and computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Join (SQL)
A join clause in SQL – corresponding to a join operation in relational algebra – combines columns from one or more tables into a new table. Informally, a join stitches two tables and puts on the same row records with matching fields : INNER, LEFT OUTER, RIGHT OUTER, FULL OUTER and CROSS. Example tables To explain join types, the rest of this article uses the following tables: Department.DepartmentID is the primary key of the Department table, whereas Employee.DepartmentID is a foreign key. Note that in Employee, "Williams" has not yet been assigned to a department. Also, no employees have been assigned to the "Marketing" department. This is the SQL statement to create the above tables: CREATE TABLE department( DepartmentID INT PRIMARY KEY NOT NULL, DepartmentName VARCHAR(20) ); CREATE TABLE employee ( LastName VARCHAR(20), DepartmentID INT REFERENCES department(DepartmentID) ); INSERT INTO department VALUES (31, 'Sales'), (33, 'Engineering'), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Table (database)
A table is a collection of related data held in a table format within a database. It consists of columns and rows. In relational databases, and flat file databases, a ''table'' is a set of data elements (values) using a model of vertical columns (identifiable by name) and horizontal rows, the cell being the unit where a row and column intersect. A table has a specified number of columns, but can have any number of rows. Each row is identified by one or more values appearing in a particular column subset. A specific choice of columns which uniquely identify rows is called the primary key. "Table" is another term for "relation"; although there is the difference in that a table is usually a multiset (bag) of rows where a relation is a set and does not allow duplicates. Besides the actual data rows, tables generally have associated with them some metadata, such as constraints on the table or on the values within particular columns. The data in a table does not have to be physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
