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Complexity Of Constraint Satisfaction
The complexity of constraint satisfaction is the application of computational complexity theory to 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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. 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 logic gate, gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
FOCS
The IEEE Annual Symposium on Foundations of Computer Science (FOCS) is an academic conference in the field of theoretical computer science. FOCS is sponsored by the IEEE Computer Society. As writes, FOCS and its annual Association for Computing Machinery counterpart STOC (the Symposium on Theory of Computing) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at FOCS and STOC as one of several defining characteristics of theoretical computer scientists. Awards The Knuth Prize for outstanding contributions to theoretical computer science is presented alternately at FOCS and STOC. Works of the highest quality presented at the conference are awarded the Best Paper Award. In addition, the Machtey Award is presented to the best student ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dichotomy
A dichotomy () is a partition of a set, 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 Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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, and decision versions o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Join (SQL)
A join clause in the Structured Query Language (SQL) combines column (database), columns from one or more table (database), tables into a new table. The operation corresponds to a Join (relational algebra), join operation in relational algebra. 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. These are the SQL statements 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 REFERENCE ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Table (database)
In a database, a table is a collection of related data organized in Table (information), table format; consisting of Column (database), columns and row (database), rows. In relational databases, and flat file databases, a ''table'' is a set of data elements (values) using a model of vertical column (database), columns (identifiable by name) and horizontal row (database), rows, the cell (database), 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 (database), "relation"; although there is the difference in that a table is usually a multiset (bag) of rows where a relation is a set (computer science), set and does not allow duplicates. Besides the actual data rows, tables generally have associated wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Conjunctive Query Containment
The subjunctive (also known as the conjunctive in some languages) is a grammatical mood, a feature of an utterance that indicates the speaker's attitude toward it. Subjunctive forms of verbs are typically used to express various states of unreality, such as wish, emotion, possibility, judgment, opinion, obligation, or action, that has not yet occurred. The precise situations in which they are used vary from language to language. The subjunctive is one of the irrealis moods, which refer to what is not necessarily real. It is often contrasted with the indicative, a realis mood which principally indicates that something is a statement of fact. Subjunctives occur most often, although not exclusively, in subordinate clauses, particularly ''that''-clauses. Examples of the subjunctive in English are found in the sentences "I suggest that you ''be'' careful" and "It is important that she ''stay'' by your side." Indo-European languages Proto-Indo-European The Proto-Indo-European language, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Relational Database
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970. A Relational Database Management System (RDBMS) is a type of database management system that stores data in a structured format using rows and columns. Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. History The concept of relational database was defined by E. F. Codd at IBM in 1970. Codd introduced the term ''relational'' in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by ''relation''. One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Primal Constraint Graph
Primal may refer to: Psychotherapy * Primal (in primal therapy), the core concept, which denotes the full reliving and cathartic release of an early traumatic experience * Primal scene (in psychoanalysis), refers to the fantasizing or witnessing by a young child of a sex act between parents 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 2016 video game Other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Tree (graph Theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A directed tree, oriented tree,See .See . polytree,See . or singly connected networkSee . is a directed acyclic graph (DAG) whose underlying undirected graph is a tree. A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. The various kinds of data structures referred to as trees in computer science have underlying graphs that are trees in graph theory, although such data structures are generally rooted trees. A rooted tree may be directed, called a directed rooted tree, either making all its edges point away from the root—in which case it is called an arborescence or out-tree� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 constraints. 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 orig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
